diff --git a/changelogs/fragments/75186-ansible-test-packaging-constraint.yml b/changelogs/fragments/75186-ansible-test-packaging-constraint.yml
new file mode 100644
index 00000000000..ef242f6a37d
--- /dev/null
+++ b/changelogs/fragments/75186-ansible-test-packaging-constraint.yml
@@ -0,0 +1,2 @@
+bugfixes:
+- "ansible-test - restrict ``packaging`` to ``< 21.0`` for Python ``< 3.6`` (https://github.com/ansible/ansible/pull/75186)."
diff --git a/test/lib/ansible_test/_data/requirements/constraints.txt b/test/lib/ansible_test/_data/requirements/constraints.txt
index 85595696435..95e8aea5ab5 100644
--- a/test/lib/ansible_test/_data/requirements/constraints.txt
+++ b/test/lib/ansible_test/_data/requirements/constraints.txt
@@ -1,3 +1,4 @@
+packaging < 21.0 ; python_version < '3.6' # packaging 21.0 requires Python 3.6 or newer
 coverage >= 4.5.1, < 5.0.0 ; python_version <  '3.7' # coverage 4.4 required for "disable_warnings" support but 4.5.1 needed for bug fixes, coverage 5.0+ incompatible
 coverage >= 4.5.2, < 5.0.0 ; python_version == '3.7' # coverage 4.5.2 fixes bugs in support for python 3.7, coverage 5.0+ incompatible
 coverage >= 4.5.4, < 5.0.0 ; python_version >  '3.7' # coverage had a bug in < 4.5.4 that would cause unit tests to hang in Python 3.8, coverage 5.0+ incompatible