diff --git a/changelogs/fragments/79187--wheel-0.38.0.yml b/changelogs/fragments/79187--wheel-0.38.0.yml
new file mode 100644
index 00000000000..62543e1868d
--- /dev/null
+++ b/changelogs/fragments/79187--wheel-0.38.0.yml
@@ -0,0 +1,2 @@
+bugfixes:
+    - ansible-test - Add ``wheel < 0.38.0`` constraint for Python 3.6 and earlier.
diff --git a/test/integration/targets/pip/meta/main.yml b/test/integration/targets/pip/meta/main.yml
index cb6005d042c..2d78e29fdbb 100644
--- a/test/integration/targets/pip/meta/main.yml
+++ b/test/integration/targets/pip/meta/main.yml
@@ -1,3 +1,4 @@
 dependencies:
   - prepare_tests
   - setup_remote_tmp_dir
+  - setup_remote_constraints
diff --git a/test/integration/targets/pip/tasks/main.yml b/test/integration/targets/pip/tasks/main.yml
index e669d297cf6..66992fd017e 100644
--- a/test/integration/targets/pip/tasks/main.yml
+++ b/test/integration/targets/pip/tasks/main.yml
@@ -37,6 +37,7 @@
     - name: ensure wheel is installed
       pip:
         name: wheel
+        extra_args: "-c {{ remote_constraints }}"
 
     - include_tasks: pip.yml
   always:
diff --git a/test/lib/ansible_test/_data/requirements/constraints.txt b/test/lib/ansible_test/_data/requirements/constraints.txt
index 6c4b53ba5de..b7b6b16f6ed 100644
--- a/test/lib/ansible_test/_data/requirements/constraints.txt
+++ b/test/lib/ansible_test/_data/requirements/constraints.txt
@@ -14,3 +14,4 @@ mock >= 2.0.0 # needed for features backported from Python 3.6 unittest.mock (as
 pytest-mock >= 1.4.0 # needed for mock_use_standalone_module pytest option
 setuptools < 45 ; python_version == '2.7' # setuptools 45 and later require python 3.5 or later
 pyspnego >= 0.1.6 ; python_version >= '3.10' # bug in older releases breaks on Python 3.10
+wheel < 0.38.0 ; python_version < '3.7' # wheel 0.38.0 and later require python 3.7 or later