diff --git a/changelogs/fragments/ansible-test-container-tmpfs.yml b/changelogs/fragments/ansible-test-container-tmpfs.yml
new file mode 100644
index 00000000000..678cd0770df
--- /dev/null
+++ b/changelogs/fragments/ansible-test-container-tmpfs.yml
@@ -0,0 +1,5 @@
+bugfixes:
+  - ansible-test - Test containers are now run with the ``--tmpfs`` option for ``/tmp``, ``/run`` and ``/run/lock``.
+                   This allows use of containers built without the ``VOLUME`` instruction.
+                   Additionally, containers with those volumes defined no longer create anonymous volumes for them.
+                   This avoids leaving behind volumes on the container host after the container is stopped and deleted.
diff --git a/test/lib/ansible_test/_internal/host_profiles.py b/test/lib/ansible_test/_internal/host_profiles.py
index cb911aef8df..50b80193397 100644
--- a/test/lib/ansible_test/_internal/host_profiles.py
+++ b/test/lib/ansible_test/_internal/host_profiles.py
@@ -428,6 +428,15 @@ class DockerProfile(ControllerHostProfile[DockerConfig], SshTargetHostProfile[Do
         options = [
             '--volume', '/sys/fs/cgroup:/sys/fs/cgroup:ro',
             f'--privileged={str(self.config.privileged).lower()}',
+            # These temporary mount points need to be created at run time.
+            # Previously they were handled by the VOLUME instruction during container image creation.
+            # However, that approach creates anonymous volumes when running the container, which are then left behind after the container is deleted.
+            # These options eliminate the need for the VOLUME instruction, and override it if they are present.
+            # The mount options used are those typically found on Linux systems.
+            # Of special note is the "exec" option for "/tmp", which is required by ansible-test for path injection of executables using temporary directories.
+            '--tmpfs', '/tmp:exec',
+            '--tmpfs', '/run:exec',
+            '--tmpfs', '/run/lock',  # some systemd containers require a separate tmpfs here, such as Ubuntu 20.04 and Ubuntu 22.04
         ]
 
         if self.config.memory: