diff --git a/multibody/parsing/BUILD.bazel b/multibody/parsing/BUILD.bazel
index e4b12c448c6e..361de302a9c3 100644
--- a/multibody/parsing/BUILD.bazel
+++ b/multibody/parsing/BUILD.bazel
@@ -86,7 +86,7 @@ drake_cc_library(
         "//geometry:proximity_properties",
         "//math:geometric_transform",
         "//multibody/plant",
-        "@sdformat",
+        "@sdformat_internal//:sdformat",
         "@tinyxml2",
     ],
 )
@@ -99,7 +99,7 @@ drake_cc_library(
     visibility = ["//visibility:private"],
     deps = [
         "//common:diagnostic_policy",
-        "@sdformat",
+        "@sdformat_internal//:sdformat",
     ],
 )
 
@@ -118,7 +118,7 @@ drake_cc_library(
         "//geometry:geometry_roles",
         "//geometry:shape_specification",
         "//multibody/plant:coulomb_friction",
-        "@sdformat",
+        "@sdformat_internal//:sdformat",
     ],
 )
 
@@ -136,7 +136,7 @@ drake_cc_library(
         ":detail_urdf_parser",
         ":scoped_names",
         "//multibody/plant",
-        "@sdformat",
+        "@sdformat_internal//:sdformat",
     ],
 )
 
diff --git a/tools/workspace/BUILD.bazel b/tools/workspace/BUILD.bazel
index a98e935e13c7..27f05d04e10d 100644
--- a/tools/workspace/BUILD.bazel
+++ b/tools/workspace/BUILD.bazel
@@ -79,8 +79,8 @@ _DRAKE_EXTERNAL_PACKAGE_INSTALLS = ["@%s//:install" % p for p in [
     "fcl",
     "fmt",
     "ghc_filesystem",
-    "ignition_math",
-    "ignition_utils",
+    "gz_math_internal",
+    "gz_utils_internal",
     "lcm",
     "meshcat",
     "meshcat_python",
@@ -89,7 +89,7 @@ _DRAKE_EXTERNAL_PACKAGE_INSTALLS = ["@%s//:install" % p for p in [
     "petsc",
     "pybind11",
     "qhull_internal",
-    "sdformat",
+    "sdformat_internal",
     "spdlog",
     "tinyobjloader",
     "usockets",
diff --git a/tools/workspace/default.bzl b/tools/workspace/default.bzl
index 818e6747e333..3297231bbc26 100644
--- a/tools/workspace/default.bzl
+++ b/tools/workspace/default.bzl
@@ -37,9 +37,9 @@ load("@drake//tools/workspace/glx:repository.bzl", "glx_repository")
 load("@drake//tools/workspace/googlebenchmark:repository.bzl", "googlebenchmark_repository")  # noqa
 load("@drake//tools/workspace/gtest:repository.bzl", "gtest_repository")
 load("@drake//tools/workspace/gurobi:repository.bzl", "gurobi_repository")
+load("@drake//tools/workspace/gz_math_internal:repository.bzl", "gz_math_internal_repository")  # noqa
+load("@drake//tools/workspace/gz_utils_internal:repository.bzl", "gz_utils_internal_repository")  # noqa
 load("@drake//tools/workspace/ibex:repository.bzl", "ibex_repository")
-load("@drake//tools/workspace/ignition_math:repository.bzl", "ignition_math_repository")  # noqa
-load("@drake//tools/workspace/ignition_utils:repository.bzl", "ignition_utils_repository")  # noqa
 load("@drake//tools/workspace/intel_realsense_ros:repository.bzl", "intel_realsense_ros_repository")  # noqa
 load("@drake//tools/workspace/ipopt:repository.bzl", "ipopt_repository")
 load("@drake//tools/workspace/json:repository.bzl", "json_repository")
@@ -80,7 +80,7 @@ load("@drake//tools/workspace/ros_xacro:repository.bzl", "ros_xacro_repository")
 load("@drake//tools/workspace/rules_pkg:repository.bzl", "rules_pkg_repository")  # noqa
 load("@drake//tools/workspace/rules_python:repository.bzl", "rules_python_repository")  # noqa
 load("@drake//tools/workspace/scs:repository.bzl", "scs_repository")
-load("@drake//tools/workspace/sdformat:repository.bzl", "sdformat_repository")
+load("@drake//tools/workspace/sdformat_internal:repository.bzl", "sdformat_internal_repository")  # noqa
 load("@drake//tools/workspace/snopt:repository.bzl", "snopt_repository")
 load("@drake//tools/workspace/spdlog:repository.bzl", "spdlog_repository")
 load("@drake//tools/workspace/stduuid:repository.bzl", "stduuid_repository")
@@ -179,12 +179,24 @@ def add_default_repositories(excludes = [], mirrors = DEFAULT_MIRRORS):
         gtest_repository(name = "gtest", mirrors = mirrors)
     if "gurobi" not in excludes:
         gurobi_repository(name = "gurobi")
+    if "gz_math_internal" not in excludes:
+        gz_math_internal_repository(name = "gz_math_internal", mirrors = mirrors)  # noqa
+    if "gz_utils_internal" not in excludes:
+        gz_utils_internal_repository(name = "gz_utils_internal", mirrors = mirrors)  # noqa
     if "ibex" not in excludes:
         ibex_repository(name = "ibex", mirrors = mirrors)
     if "ignition_math" not in excludes:
-        ignition_math_repository(name = "ignition_math", mirrors = mirrors)
+        add_deprecation(
+            name = "ignition_math",
+            date = "2022-10-01",
+            cc_aliases = {"ignition_math": "@gz_math_internal//:gz_math"},
+        )
     if "ignition_utils" not in excludes:
-        ignition_utils_repository(name = "ignition_utils", mirrors = mirrors)
+        add_deprecation(
+            name = "ignition_utils",
+            date = "2022-10-01",
+            cc_aliases = {"ignition_utils": "@gz_utils_internal//:gz_utils"},
+        )
     if "intel_realsense_ros" not in excludes:
         intel_realsense_ros_repository(name = "intel_realsense_ros", mirrors = mirrors)  # noqa
     if "ipopt" not in excludes:
@@ -272,7 +284,13 @@ def add_default_repositories(excludes = [], mirrors = DEFAULT_MIRRORS):
     if "scs" not in excludes:
         scs_repository(name = "scs", mirrors = mirrors)
     if "sdformat" not in excludes:
-        sdformat_repository(name = "sdformat", mirrors = mirrors)
+        add_deprecation(
+            name = "sdformat",
+            date = "2022-10-01",
+            cc_aliases = {"sdformat": "@sdformat_internal//:sdformat"},
+        )
+    if "sdformat_internal" not in excludes:
+        sdformat_internal_repository(name = "sdformat_internal", mirrors = mirrors)  # noqa
     if "snopt" not in excludes:
         snopt_repository(name = "snopt")
     if "spdlog" not in excludes:
diff --git a/tools/workspace/ignition_math/BUILD.bazel b/tools/workspace/gz_math_internal/BUILD.bazel
similarity index 100%
rename from tools/workspace/ignition_math/BUILD.bazel
rename to tools/workspace/gz_math_internal/BUILD.bazel
diff --git a/tools/workspace/ignition_math/package.BUILD.bazel b/tools/workspace/gz_math_internal/package.BUILD.bazel
similarity index 99%
rename from tools/workspace/ignition_math/package.BUILD.bazel
rename to tools/workspace/gz_math_internal/package.BUILD.bazel
index 76341dbc9a1f..d2fdf029d7a4 100644
--- a/tools/workspace/ignition_math/package.BUILD.bazel
+++ b/tools/workspace/gz_math_internal/package.BUILD.bazel
@@ -159,7 +159,7 @@ public_headers = public_headers_no_gen + [
 # explicitly listed sources plus private headers.  The explicitly listed
 # hdrs= matches upstream's public headers.
 cc_library(
-    name = "ignition_math",
+    name = "gz_math",
     srcs = [
         "src/Angle.cc",
         "src/AxisAlignedBox.cc",
diff --git a/tools/workspace/ignition_math/repository.bzl b/tools/workspace/gz_math_internal/repository.bzl
similarity index 73%
rename from tools/workspace/ignition_math/repository.bzl
rename to tools/workspace/gz_math_internal/repository.bzl
index f73311d54619..9a1d71db46f4 100644
--- a/tools/workspace/ignition_math/repository.bzl
+++ b/tools/workspace/gz_math_internal/repository.bzl
@@ -2,8 +2,7 @@
 
 load("//tools/workspace:github.bzl", "github_archive")
 
-# TODO(jwnimmer-tri) Rename this to match upstream gz-math.
-def ignition_math_repository(
+def gz_math_internal_repository(
         name,
         mirrors = None):
     # When updating this commit, also remember to adjust the PROJECT_*
@@ -13,6 +12,6 @@ def ignition_math_repository(
         repository = "gazebosim/gz-math",
         commit = "ignition-math6_6.10.0",
         sha256 = "94e853e1dfba97ebec4b6152691a89af1e94660b02f4ecdf04356b763c2848bd",  # noqa
-        build_file = "@drake//tools/workspace/ignition_math:package.BUILD.bazel",  # noqa
+        build_file = "@drake//tools/workspace/gz_math_internal:package.BUILD.bazel",  # noqa
         mirrors = mirrors,
     )
diff --git a/tools/workspace/ignition_utils/BUILD.bazel b/tools/workspace/gz_utils_internal/BUILD.bazel
similarity index 100%
rename from tools/workspace/ignition_utils/BUILD.bazel
rename to tools/workspace/gz_utils_internal/BUILD.bazel
diff --git a/tools/workspace/ignition_utils/package.BUILD.bazel b/tools/workspace/gz_utils_internal/package.BUILD.bazel
similarity index 98%
rename from tools/workspace/ignition_utils/package.BUILD.bazel
rename to tools/workspace/gz_utils_internal/package.BUILD.bazel
index 2ce8f04787d8..1a24f95b7cc6 100644
--- a/tools/workspace/ignition_utils/package.BUILD.bazel
+++ b/tools/workspace/gz_utils_internal/package.BUILD.bazel
@@ -87,7 +87,7 @@ public_headers = public_headers_no_gen + [
 ]
 
 cc_library(
-    name = "ignition_utils",
+    name = "gz_utils",
     srcs = private_headers,
     hdrs = public_headers,
     includes = ["include"],
diff --git a/tools/workspace/ignition_utils/repository.bzl b/tools/workspace/gz_utils_internal/repository.bzl
similarity index 73%
rename from tools/workspace/ignition_utils/repository.bzl
rename to tools/workspace/gz_utils_internal/repository.bzl
index ed6fcc6d343f..03cd32e5f05a 100644
--- a/tools/workspace/ignition_utils/repository.bzl
+++ b/tools/workspace/gz_utils_internal/repository.bzl
@@ -2,8 +2,7 @@
 
 load("//tools/workspace:github.bzl", "github_archive")
 
-# TODO(jwnimmer-tri) Rename this to match upstream gz-utils.
-def ignition_utils_repository(
+def gz_utils_internal_repository(
         name,
         mirrors = None):
     github_archive(
@@ -13,6 +12,6 @@ def ignition_utils_repository(
         # constants in ./package.BUILD.bazel to match the new version number.
         commit = "ignition-utils1_1.0.0",
         sha256 = "55d3285692392f9493a35b680f275ec116584baedeef90de57d2b03dfd952d9d",  # noqa
-        build_file = "@drake//tools/workspace/ignition_utils:package.BUILD.bazel",  # noqa
+        build_file = "@drake//tools/workspace/gz_utils_internal:package.BUILD.bazel",  # noqa
         mirrors = mirrors,
     )
diff --git a/tools/workspace/new_release.py b/tools/workspace/new_release.py
index f60846ba4111..4a278a855619 100644
--- a/tools/workspace/new_release.py
+++ b/tools/workspace/new_release.py
@@ -65,14 +65,14 @@
 # (This can be used to pin to a given major or major.minor release series.)
 _OVERLOOK_RELEASE_REPOSITORIES = {
     "github3_py": r"^(\d+.)",
-    "ignition_math": "",
-    "ignition_utils": "",
+    "gz_math": "",
+    "gz_utils": "",
     "intel_realsense_ros": r"^(\d+\.\d+\.)",
     "petsc": r"^(v)",
     "pycodestyle": "",
-    "qhull": r"^(2)",
+    "qhull_internal": r"^(2)",
     "ros_xacro": r"^(\d+\.\d+\.)",
-    "sdformat": "",
+    "sdformat_internal": "",
 }
 
 
diff --git a/tools/workspace/sdformat/repository.bzl b/tools/workspace/sdformat/repository.bzl
deleted file mode 100644
index a01d618447dd..000000000000
--- a/tools/workspace/sdformat/repository.bzl
+++ /dev/null
@@ -1,21 +0,0 @@
-# -*- python -*-
-
-load("//tools/workspace:github.bzl", "github_archive")
-
-def sdformat_repository(
-        name,
-        mirrors = None):
-    github_archive(
-        name = name,
-        repository = "gazebosim/sdformat",
-        commit = "sdformat12_12.5.0",
-        build_file = "@drake//tools/workspace/sdformat:package.BUILD.bazel",
-        sha256 = "3896772db68b7ca7b18bbf1945a72206885b03d3f0caf29491be5b53b79a7124",  # noqa
-        patches = [
-            "@drake//tools/workspace/sdformat:patches/console.patch",
-            "@drake//tools/workspace/sdformat:patches/deprecation_unit_testing.patch",  # noqa
-            "@drake//tools/workspace/sdformat:patches/no_global_config.patch",
-            "@drake//tools/workspace/sdformat:patches/no_urdf.patch",
-        ],
-        mirrors = mirrors,
-    )
diff --git a/tools/workspace/sdformat/BUILD.bazel b/tools/workspace/sdformat_internal/BUILD.bazel
similarity index 82%
rename from tools/workspace/sdformat/BUILD.bazel
rename to tools/workspace/sdformat_internal/BUILD.bazel
index d4b739ac34f4..df9c31528512 100644
--- a/tools/workspace/sdformat/BUILD.bazel
+++ b/tools/workspace/sdformat_internal/BUILD.bazel
@@ -6,7 +6,7 @@ load("//tools/lint:lint.bzl", "add_lint_tests")
 
 exports_files(
     ["embed_sdf.py"],
-    visibility = ["@sdformat//:__pkg__"],
+    visibility = ["@sdformat_internal//:__pkg__"],
 )
 
 drake_cc_binary(
@@ -15,7 +15,7 @@ drake_cc_binary(
     deps = [
         "//common:essential",
         "@gflags",
-        "@sdformat//:ign_sdf_cmdline",
+        "@sdformat_internal//:ign_sdf_cmdline",
     ],
 )
 
diff --git a/tools/workspace/sdformat/embed_sdf.py b/tools/workspace/sdformat_internal/embed_sdf.py
similarity index 100%
rename from tools/workspace/sdformat/embed_sdf.py
rename to tools/workspace/sdformat_internal/embed_sdf.py
diff --git a/tools/workspace/sdformat/ign_sdf_main.cc b/tools/workspace/sdformat_internal/ign_sdf_main.cc
similarity index 100%
rename from tools/workspace/sdformat/ign_sdf_main.cc
rename to tools/workspace/sdformat_internal/ign_sdf_main.cc
diff --git a/tools/workspace/sdformat/package.BUILD.bazel b/tools/workspace/sdformat_internal/package.BUILD.bazel
similarity index 98%
rename from tools/workspace/sdformat/package.BUILD.bazel
rename to tools/workspace/sdformat_internal/package.BUILD.bazel
index 8c9aadc7fd56..f1edb8b647cc 100644
--- a/tools/workspace/sdformat/package.BUILD.bazel
+++ b/tools/workspace/sdformat_internal/package.BUILD.bazel
@@ -134,7 +134,7 @@ genrule(
 
 py_binary(
     name = "embed_sdf",
-    srcs = ["@drake//tools/workspace/sdformat:embed_sdf.py"],
+    srcs = ["@drake//tools/workspace/sdformat_internal:embed_sdf.py"],
     python_version = "PY3",
     srcs_version = "PY3",
 )
@@ -241,8 +241,8 @@ cc_library(
     includes = ["include"],
     linkstatic = 1,
     deps = [
-        "@ignition_math",
-        "@ignition_utils",
+        "@gz_math_internal//:gz_math",
+        "@gz_utils_internal//:gz_utils",
         "@tinyxml2",
         # N.B. It's very unusual to add a dependency from a third-party library
         # onto Drake, but in this case it's the simplest way to be able to send
diff --git a/tools/workspace/sdformat/patches/console.patch b/tools/workspace/sdformat_internal/patches/console.patch
similarity index 100%
rename from tools/workspace/sdformat/patches/console.patch
rename to tools/workspace/sdformat_internal/patches/console.patch
diff --git a/tools/workspace/sdformat/patches/deprecation_unit_testing.patch b/tools/workspace/sdformat_internal/patches/deprecation_unit_testing.patch
similarity index 100%
rename from tools/workspace/sdformat/patches/deprecation_unit_testing.patch
rename to tools/workspace/sdformat_internal/patches/deprecation_unit_testing.patch
diff --git a/tools/workspace/sdformat/patches/no_global_config.patch b/tools/workspace/sdformat_internal/patches/no_global_config.patch
similarity index 100%
rename from tools/workspace/sdformat/patches/no_global_config.patch
rename to tools/workspace/sdformat_internal/patches/no_global_config.patch
diff --git a/tools/workspace/sdformat/patches/no_urdf.patch b/tools/workspace/sdformat_internal/patches/no_urdf.patch
similarity index 100%
rename from tools/workspace/sdformat/patches/no_urdf.patch
rename to tools/workspace/sdformat_internal/patches/no_urdf.patch
diff --git a/tools/workspace/sdformat_internal/repository.bzl b/tools/workspace/sdformat_internal/repository.bzl
new file mode 100644
index 000000000000..35d98edb2a83
--- /dev/null
+++ b/tools/workspace/sdformat_internal/repository.bzl
@@ -0,0 +1,21 @@
+# -*- python -*-
+
+load("//tools/workspace:github.bzl", "github_archive")
+
+def sdformat_internal_repository(
+        name,
+        mirrors = None):
+    github_archive(
+        name = name,
+        repository = "gazebosim/sdformat",
+        commit = "sdformat12_12.5.0",
+        build_file = "@drake//tools/workspace/sdformat_internal:package.BUILD.bazel",  # noqa
+        sha256 = "3896772db68b7ca7b18bbf1945a72206885b03d3f0caf29491be5b53b79a7124",  # noqa
+        patches = [
+            "@drake//tools/workspace/sdformat_internal:patches/console.patch",
+            "@drake//tools/workspace/sdformat_internal:patches/deprecation_unit_testing.patch",  # noqa
+            "@drake//tools/workspace/sdformat_internal:patches/no_global_config.patch",  # noqa
+            "@drake//tools/workspace/sdformat_internal:patches/no_urdf.patch",
+        ],
+        mirrors = mirrors,
+    )
diff --git a/tools/workspace/sdformat/test/ign_sdf_test.py b/tools/workspace/sdformat_internal/test/ign_sdf_test.py
similarity index 97%
rename from tools/workspace/sdformat/test/ign_sdf_test.py
rename to tools/workspace/sdformat_internal/test/ign_sdf_test.py
index e13e2a7e5491..1bfc0bfecdd6 100644
--- a/tools/workspace/sdformat/test/ign_sdf_test.py
+++ b/tools/workspace/sdformat_internal/test/ign_sdf_test.py
@@ -57,7 +57,7 @@
 class TestIgnSdf(unittest.TestCase):
     def setUp(self):
         self.maxDiff = None
-        self.bin = "tools/workspace/sdformat/ign_sdf"
+        self.bin = "tools/workspace/sdformat_internal/ign_sdf"
         self.input_file = os.path.join(
             os.environ["TEST_TMPDIR"], "example.sdf"
         )