diff --git a/tests/test_signer.py b/tests/test_signer.py
index 3cb644bd..b52ad1cc 100644
--- a/tests/test_signer.py
+++ b/tests/test_signer.py
@@ -17,12 +17,27 @@
     Test cases for 'signer.py'.
 """
 
+import sys
+import unittest
+
 import unittest
 import securesystemslib.formats
 import securesystemslib.keys as KEYS
-from securesystemslib.signer import Signature, SSlibSigner
 from securesystemslib.exceptions import FormatError, UnsupportedAlgorithmError
 
+# TODO: Remove case handling when fully dropping support for versions >= 3.6
+IS_PY_VERSION_SUPPORTED = sys.version_info >= (3, 6)
+
+# Use setUpModule to tell unittest runner to skip this test module gracefully.
+def setUpModule():
+    if not IS_PY_VERSION_SUPPORTED:
+        raise unittest.SkipTest('requires Python 3.6 or higher')
+
+# Since setUpModule is called after imports we need to import conditionally.
+if IS_PY_VERSION_SUPPORTED:
+    from securesystemslib.signer import Signature, SSlibSigner
+
+
 class TestSSlibSigner(unittest.TestCase):
 
     @classmethod