diff --git a/Lib/test/test_hashlib.py b/Lib/test/test_hashlib.py
index 56d2f70021235f..8eb0ac230bc770 100644
--- a/Lib/test/test_hashlib.py
+++ b/Lib/test/test_hashlib.py
@@ -264,7 +264,10 @@ def test_clinic_signature(self):
                 hashlib.new(digest_name, b'')
                 hashlib.new(digest_name, data=b'')
                 hashlib.new(digest_name, string=b'')
-                if self._hashlib:
+                # Make sure that _hashlib contains the constructor
+                # to test when using a combination of libcrypto and
+                # interned hash implementations.
+                if self._hashlib and digest_name in self._hashlib._constructors:
                     self._hashlib.new(digest_name, b'')
                     self._hashlib.new(digest_name, data=b'')
                     self._hashlib.new(digest_name, string=b'')
@@ -316,7 +319,8 @@ def test_clinic_signature_errors(self):
                 with self.subTest(digest_name, args=args, kwds=kwds):
                     with self.assertRaisesRegex(TypeError, errmsg):
                         hashlib.new(digest_name, *args, **kwds)
-                    if self._hashlib:
+                    if (self._hashlib and
+                            digest_name in self._hashlib._constructors):
                         with self.assertRaisesRegex(TypeError, errmsg):
                             self._hashlib.new(digest_name, *args, **kwds)