diff --git a/setup/BUILD.bazel b/setup/BUILD.bazel
index ca1656cedaf6..2521b0a733f1 100644
--- a/setup/BUILD.bazel
+++ b/setup/BUILD.bazel
@@ -19,10 +19,12 @@ exports_files([
     "ubuntu/binary_distribution/packages-bionic.txt",
     "ubuntu/binary_distribution/packages-focal.txt",
     "ubuntu/source_distribution/packages-bionic.txt",
+    "ubuntu/source_distribution/packages-bionic-clang.txt",
     "ubuntu/source_distribution/packages-bionic-doc-only.txt",
     "ubuntu/source_distribution/packages-bionic-maintainer-only.txt",
     "ubuntu/source_distribution/packages-bionic-test-only.txt",
     "ubuntu/source_distribution/packages-focal.txt",
+    "ubuntu/source_distribution/packages-focal-clang.txt",
     "ubuntu/source_distribution/packages-focal-doc-only.txt",
     "ubuntu/source_distribution/packages-focal-maintainer-only.txt",
     "ubuntu/source_distribution/packages-focal-test-only.txt",
diff --git a/setup/ubuntu/install_prereqs.sh b/setup/ubuntu/install_prereqs.sh
index fb15cc13783d..f50f51a3a36a 100755
--- a/setup/ubuntu/install_prereqs.sh
+++ b/setup/ubuntu/install_prereqs.sh
@@ -31,16 +31,21 @@ while [ "${1:-}" != "" ]; do
     --with-kcov)
       source_distribution_args+=(--with-kcov)
       ;;
+    # Install prerequisites that are only needed to when CC=clang-9, i.e.,
+    # opts-in to the ability to compile Drake's C++ code using Clang.
+    --with-clang)
+      source_distribution_args+=(--with-clang)
+      ;;
+    # Do NOT install prerequisites that are only needed to when CC=clang-9,
+    # i.e., opts-out of the ability to compile Drake's C++ code using Clang.
+    --without-clang)
+      source_distribution_args+=(--without-clang)
+      ;;
     # Install prerequisites that are only needed to run select maintainer
     # scripts. Most developers will not need to install these dependencies.
     --with-maintainer-only)
       source_distribution_args+=(--with-maintainer-only)
       ;;
-    # Do NOT install prerequisites that are only needed to build documentation,
-    # i.e., those prerequisites that are dependencies of bazel run //doc:build.
-    --without-doc-only)
-      source_distribution_args+=(--without-doc-only)
-      ;;
     # Do NOT install prerequisites that are only needed to build and/or run
     # unit tests, i.e., those prerequisites that are not dependencies of
     # bazel { build, run } //:install.
diff --git a/setup/ubuntu/source_distribution/install_prereqs.sh b/setup/ubuntu/source_distribution/install_prereqs.sh
index d120809fa9ad..d7d67422b479 100755
--- a/setup/ubuntu/source_distribution/install_prereqs.sh
+++ b/setup/ubuntu/source_distribution/install_prereqs.sh
@@ -11,10 +11,13 @@ set -euo pipefail
 with_doc_only=0
 with_kcov=0
 with_maintainer_only=0
+with_clang=1
 with_test_only=1
 with_update=1
 with_asking=1
 
+# TODO(jwnimmer-tri) Eventually we should default to with_clang=0.
+
 while [ "${1:-}" != "" ]; do
   case "$1" in
     # Install prerequisites that are only needed to build documentation,
@@ -29,6 +32,16 @@ while [ "${1:-}" != "" ]; do
     --with-kcov)
       with_kcov=1
       ;;
+    # Install prerequisites that are only needed to when CC=clang-9, i.e.,
+    # opts-in to the ability to compile Drake's C++ code using Clang.
+    --with-clang)
+      with_clang=1
+      ;;
+    # Do NOT install prerequisites that are only needed to when CC=clang-9,
+    # i.e., opts-out of the ability to compile Drake's C++ code using Clang.
+    --without-clang)
+      with_clang=0
+      ;;
     # Install prerequisites that are only needed to run select maintainer
     # scripts. Most developers will not need to install these dependencies.
     --with-maintainer-only)
@@ -124,6 +137,11 @@ if [[ "${with_doc_only}" -eq 1 ]]; then
   apt-get install ${maybe_yes} --no-install-recommends ${packages}
 fi
 
+if [[ "${with_clang}" -eq 1 ]]; then
+  packages=$(cat "${BASH_SOURCE%/*}/packages-${codename}-clang.txt")
+  apt-get install ${maybe_yes} --no-install-recommends ${packages}
+fi
+
 if [[ "${with_test_only}" -eq 1 ]]; then
   packages=$(cat "${BASH_SOURCE%/*}/packages-${codename}-test-only.txt")
   # Suppress Python 3.8 warnings when installing python3-pandas on Focal.
diff --git a/setup/ubuntu/source_distribution/packages-bionic-clang.txt b/setup/ubuntu/source_distribution/packages-bionic-clang.txt
new file mode 100644
index 000000000000..5db5152c0670
--- /dev/null
+++ b/setup/ubuntu/source_distribution/packages-bionic-clang.txt
@@ -0,0 +1,2 @@
+clang-9
+libomp-9-dev
diff --git a/setup/ubuntu/source_distribution/packages-bionic.txt b/setup/ubuntu/source_distribution/packages-bionic.txt
index a5c2881a66e3..86650c85f788 100644
--- a/setup/ubuntu/source_distribution/packages-bionic.txt
+++ b/setup/ubuntu/source_distribution/packages-bionic.txt
@@ -1,4 +1,3 @@
-clang-9
 clang-format-9
 coinor-libclp-dev
 coinor-libcoinutils-dev
diff --git a/setup/ubuntu/source_distribution/packages-focal-clang.txt b/setup/ubuntu/source_distribution/packages-focal-clang.txt
new file mode 100644
index 000000000000..5db5152c0670
--- /dev/null
+++ b/setup/ubuntu/source_distribution/packages-focal-clang.txt
@@ -0,0 +1,2 @@
+clang-9
+libomp-9-dev
diff --git a/setup/ubuntu/source_distribution/packages-focal.txt b/setup/ubuntu/source_distribution/packages-focal.txt
index 5cfb58cabce1..9a5371e9be6b 100644
--- a/setup/ubuntu/source_distribution/packages-focal.txt
+++ b/setup/ubuntu/source_distribution/packages-focal.txt
@@ -1,4 +1,3 @@
-clang-9
 clang-format-9
 coinor-libclp-dev
 coinor-libcoinutils-dev