diff --git a/common/BUILD.bazel b/common/BUILD.bazel
index 3b62daf1d457..ad0c09cb3244 100644
--- a/common/BUILD.bazel
+++ b/common/BUILD.bazel
@@ -30,6 +30,7 @@ drake_cc_package_library(
         ":diagnostic_policy",
         ":double",
         ":drake_bool",
+        ":drake_export",
         ":drake_path",
         ":dummy_value",
         ":essential",
@@ -190,6 +191,11 @@ drake_cc_library(
 
 # Miscellaneous utilities.
 
+drake_cc_library(
+    name = "drake_export",
+    hdrs = ["drake_export.h"],
+)
+
 drake_cc_library(
     name = "identifier",
     srcs = ["identifier.cc"],
diff --git a/common/drake_export.h b/common/drake_export.h
new file mode 100644
index 000000000000..d42cc9c2a36e
--- /dev/null
+++ b/common/drake_export.h
@@ -0,0 +1,39 @@
+#pragma once
+
+/** DRAKE_NO_EXPORT sets C++ code to use hidden linker visibility.
+
+Hidden visibility is appropriate for code that will be completely invisible to
+users, e.g., for header files that are bazel-private, not installed, and only
+used as implementation_deps.
+
+This macro is most useful when Drake code includes externals that themselves
+have hidden linker visibility and compilers complain about mismatched
+visibility attributes.
+
+For example, to un-export all classes and functions in a namespace:
+<pre>
+namespace internal DRAKE_NO_EXPORT {
+class Foo {
+  // ...
+};
+}  // namespace internal
+</pre>
+
+To un-export just one class:
+<pre>
+namespace internal {
+class DRAKE_NO_EXPORT Foo {
+  // ...
+};
+}  // namespace internal
+</pre>
+
+To un-export just one function:
+<pre>
+DRAKE_NO_EXPORT void CalcFoo(double arg) { ... }
+</pre>
+
+For the related CMake module, see:
+https://cmake.org/cmake/help/latest/module/GenerateExportHeader.html
+*/
+#define DRAKE_NO_EXPORT __attribute__((visibility("hidden")))
diff --git a/geometry/BUILD.bazel b/geometry/BUILD.bazel
index 03545843bdbc..8befa9cea120 100644
--- a/geometry/BUILD.bazel
+++ b/geometry/BUILD.bazel
@@ -466,6 +466,7 @@ drake_cc_library(
         "//perception:point_cloud",
     ],
     deps = [
+        "//common:drake_export",
         "//common:find_resource",
         "//common:scope_exit",
         "//common:unused",
diff --git a/geometry/meshcat.cc b/geometry/meshcat.cc
index 570acd1ae78b..a9e0154acc9f 100644
--- a/geometry/meshcat.cc
+++ b/geometry/meshcat.cc
@@ -24,6 +24,7 @@
 #include <drake_vendor/uuid.h>
 #include <fmt/format.h>
 
+#include "drake/common/drake_export.h"
 #include "drake/common/drake_throw.h"
 #include "drake/common/find_resource.h"
 #include "drake/common/never_destroyed.h"
@@ -1088,10 +1089,8 @@ class Meshcat::Impl {
     });
   }
 
-  // This function is public via the PIMPL. We'll set linker visibility to
-  // avoid a warning about our std::visit's lambda capture of a msgpack object.
-  __attribute__((visibility("hidden")))
-  void SetAnimation(const MeshcatAnimation& animation) {
+  // This function is public via the PIMPL.
+  DRAKE_NO_EXPORT void SetAnimation(const MeshcatAnimation& animation) {
     DRAKE_DEMAND(IsThread(main_thread_id_));
 
     std::stringstream message_stream;
diff --git a/tools/skylark/drake_cc.bzl b/tools/skylark/drake_cc.bzl
index f2be352f0bda..213a68b67ffc 100644
--- a/tools/skylark/drake_cc.bzl
+++ b/tools/skylark/drake_cc.bzl
@@ -7,6 +7,7 @@ load("//tools/skylark:kwargs.bzl", "incorporate_num_threads")
 # building with any compiler.
 CXX_FLAGS = [
     "-Werror=all",
+    "-Werror=attributes",
     "-Werror=cpp",
     "-Werror=deprecated",
     "-Werror=deprecated-declarations",