diff --git a/changelogs/fragments/ansible-test-pyopenssl.yaml b/changelogs/fragments/ansible-test-pyopenssl.yaml
new file mode 100644
index 00000000000..f05ef8ead33
--- /dev/null
+++ b/changelogs/fragments/ansible-test-pyopenssl.yaml
@@ -0,0 +1,2 @@
+bugfixes:
+  - ansible-test - When installing ``cryptography < 3.4`` also install ``pyopenssl < 22`` to avoid conflicts.
diff --git a/test/lib/ansible_test/_internal/python_requirements.py b/test/lib/ansible_test/_internal/python_requirements.py
index e1b74ebd7f5..409851fe745 100644
--- a/test/lib/ansible_test/_internal/python_requirements.py
+++ b/test/lib/ansible_test/_internal/python_requirements.py
@@ -455,8 +455,8 @@ def get_cryptography_requirements(python):  # type: (PythonConfig) -> t.List[str
         # cryptography 3.4+ fails to install on many systems
         # this is a temporary work-around until a more permanent solution is available
         cryptography = 'cryptography < 3.4'
-        # no specific version of pyopenssl required, don't install it
-        pyopenssl = None
+        # pyopenssl 20.0.0 requires cryptography 35 or later
+        pyopenssl = 'pyopenssl < 22.0.0'
 
     requirements = [
         cryptography,