diff --git a/tools/workspace/spdlog/BUILD.bazel b/tools/workspace/spdlog/BUILD.bazel
index 9459bb43c43d..7198e3bb9b53 100644
--- a/tools/workspace/spdlog/BUILD.bazel
+++ b/tools/workspace/spdlog/BUILD.bazel
@@ -2,12 +2,4 @@
 
 load("//tools/lint:lint.bzl", "add_lint_tests")
 
-exports_files(
-    [
-        "spdlog-config.cmake",
-        "spdlog-config-version.cmake",
-    ],
-    visibility = ["@spdlog//:__pkg__"],
-)
-
 add_lint_tests()
diff --git a/tools/workspace/spdlog/package.BUILD.bazel b/tools/workspace/spdlog/package.BUILD.bazel
index 68b2d5b3ad09..a4b66b9e695b 100644
--- a/tools/workspace/spdlog/package.BUILD.bazel
+++ b/tools/workspace/spdlog/package.BUILD.bazel
@@ -6,7 +6,6 @@
 load(
     "@drake//tools/install:install.bzl",
     "install",
-    "install_files",
 )
 
 licenses(["notice"])  # MIT
@@ -92,27 +91,12 @@ cc_library(
     visibility = ["//visibility:public"],
 )
 
-CMAKE_PACKAGE = "spdlog"
-
-install_files(
-    name = "install_cmake_config",
-    dest = "lib/cmake/{}".format(CMAKE_PACKAGE),
-    files = [
-        "@drake//tools/workspace/spdlog:{}-config.cmake".format(CMAKE_PACKAGE),  # noqa
-        "@drake//tools/workspace/spdlog:{}-config-version.cmake".format(CMAKE_PACKAGE),  # noqa
-    ],
-    strip_prefix = ["**/"],
-    allowed_externals = ["@drake//:.bazelproject"],
-    visibility = ["//visibility:private"],
-)
-
 install(
     name = "install",
     targets = [":libdrake_spdlog.so"],
-    hdr_dest = "include/" + CMAKE_PACKAGE,
+    hdr_dest = "include/spdlog",
     hdr_strip_prefix = ["include"],
     hdrs = _HDRS,
     docs = ["LICENSE"],
-    deps = [":install_cmake_config"],
     visibility = ["//visibility:public"],
 )
diff --git a/tools/workspace/spdlog/repository.bzl b/tools/workspace/spdlog/repository.bzl
index f8d728cf6073..7ceee5437069 100644
--- a/tools/workspace/spdlog/repository.bzl
+++ b/tools/workspace/spdlog/repository.bzl
@@ -28,7 +28,7 @@ def _impl(repo_ctx):
 
 spdlog_repository = repository_rule(
     attrs = {
-        # The next two attributes are used only when we take the branch for
+        # The next several attributes are used only when we take the branch for
         # setup_pkg_config_repository in the above logic.
         "modname": attr.string(
             default = "spdlog",
@@ -55,10 +55,6 @@ install(name = "install")
             # Here, we elect to use the same version as Ubuntu 20.04, even
             # though it is not the newest revision.  Sticking with a single,
             # older revision helps reduce spurious CI failures.
-            #
-            # In the unlikely event that you update the version here, fix up
-            # the two spdlog-*.cmake files in this directory, and revisit all
-            # of the version compatibility matrix in spdlog/repository.bzl.
             default = "v1.5.0",
         ),
         "commit_pin": attr.int(
diff --git a/tools/workspace/spdlog/spdlog-config-version.cmake b/tools/workspace/spdlog/spdlog-config-version.cmake
deleted file mode 100644
index 53cfd5911976..000000000000
--- a/tools/workspace/spdlog/spdlog-config-version.cmake
+++ /dev/null
@@ -1,19 +0,0 @@
-# This file is only used in cases when we need to rebuild spdlog from source.
-# See repository.bzl for the logic to select when that occurs.
-
-set(PACKAGE_VERSION "1.5.0")
-set(PACKAGE_COMPAT_VERSION "1.5.0")
-
-if(PACKAGE_VERSION VERSION_LESS PACKAGE_FIND_VERSION)
-  set(PACKAGE_VERSION_COMPATIBLE FALSE)
-elseif(PACKAGE_VERSION VERSION_LESS COMPAT_VERSION)
-  set(PACKAGE_VERSION_COMPATIBLE FALSE)
-else()
-  set(PACKAGE_VERSION_COMPATIBLE TRUE)
-  if(PACKAGE_VERSION STREQUAL PACKAGE_FIND_VERSION)
-    set(PACKAGE_VERSION_EXACT TRUE)
-  endif()
-endif()
-
-unset(PACKAGE_COMPAT_VERSION)
-
diff --git a/tools/workspace/spdlog/spdlog-config.cmake b/tools/workspace/spdlog/spdlog-config.cmake
deleted file mode 100644
index 598e8ea5a5dd..000000000000
--- a/tools/workspace/spdlog/spdlog-config.cmake
+++ /dev/null
@@ -1,74 +0,0 @@
-# This file is only used in cases when we need to rebuild spdlog from source.
-# See repository.bzl for the logic to select when that occurs.
-
-# Generated by cps2cmake https://github.com/mwoehlke/pycps
-# and then subsequently edited by hand.
-
-if(CMAKE_VERSION VERSION_LESS 3.9.0)
-  message(FATAL_ERROR "CMake >= 3.9 required")
-endif()
-cmake_policy(PUSH)
-cmake_policy(VERSION 3.0)
-set(CMAKE_IMPORT_FILE_VERSION 1)
-
-include(CMakeFindDependencyMacro)
-
-get_filename_component(${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX "${CMAKE_CURRENT_LIST_FILE}" PATH)
-get_filename_component(${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX "${${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX}" PATH)
-get_filename_component(${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX "${${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX}" PATH)
-get_filename_component(${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX "${${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX}" PATH)
-
-if(${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX STREQUAL "/")
-  set(${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX)
-endif()
-
-find_dependency(fmt 6.1.2 CONFIG HINTS "${${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX}/lib/cmake/fmt")
-set(_expectedTargets spdlog::spdlog)
-
-set(_targetsDefined)
-set(_targetsNotDefined)
-
-foreach(_expectedTarget ${_expectedTargets})
-  if(NOT TARGET ${_expectedTarget})
-    list(APPEND _targetsNotDefined ${_expectedTarget})
-  endif()
-  if(TARGET ${_expectedTarget})
-    list(APPEND _targetsDefined ${_expectedTarget})
-  endif()
-endforeach()
-if("${_targetsDefined}" STREQUAL "${_expectedTargets}")
-  set(CMAKE_IMPORT_FILE_VERSION)
-  cmake_policy(POP)
-  return()
-endif()
-if(NOT "${_targetsDefined}" STREQUAL "")
-  message(FATAL_ERROR "Some (but not all) targets in this export set were already defined.\nTargets Defined: ${_targetsDefined}\nTargets not yet defined: ${_targetsNotDefined}\n")
-endif()
-unset(_targetsDefined)
-unset(_targetsNotDefined)
-unset(_expectedTargets)
-
-set(spdlog_VERSION "1.5.0")
-
-set(_apple_soname_prologue)
-if(APPLE)
-  set(_apple_soname_prologue "@rpath/")
-endif()
-add_library(spdlog::spdlog SHARED IMPORTED)
-set_target_properties(spdlog::spdlog PROPERTIES
-  IMPORTED_LOCATION "${${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX}/lib/libdrake_spdlog.so"
-  IMPORTED_SONAME "${_apple_soname_prologue}libdrake_spdlog.so"
-  INTERFACE_INCLUDE_DIRECTORIES "${${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX}/include/spdlog"
-  INTERFACE_LINK_LIBRARIES "fmt::fmt-header-only"
-  INTERFACE_COMPILE_DEFINITIONS "HAVE_SPDLOG;SPDLOG_COMPILED_LIB;SPDLOG_FMT_EXTERNAL"
-)
-unset(_apple_soname_prologue)
-
-set(spdlog_LIBRARIES "spdlog::spdlog")
-set(spdlog_INCLUDE_DIRS "")
-
-
-unset(${CMAKE_FIND_PACKAGE_NAME}_IMPORT_PREFIX)
-unset(CMAKE_IMPORT_FILE_VERSION)
-cmake_policy(POP)
-