diff --git a/Lib/test/test_hashlib.py b/Lib/test/test_hashlib.py
index 0fecc95fec40fc..14a79a1c698ffb 100644
--- a/Lib/test/test_hashlib.py
+++ b/Lib/test/test_hashlib.py
@@ -41,12 +41,15 @@
 openssl_hashlib = import_fresh_module('hashlib', fresh=['_hashlib'])
 
 try:
-    from _hashlib import HASH, HASHXOF, openssl_md_meth_names, get_fips_mode
+    import _hashlib
 except ImportError:
-    HASH = None
-    HASHXOF = None
-    openssl_md_meth_names = frozenset()
-
+    _hashlib = None
+# The extension module may exist but only define some of these. gh-141907
+HASH = getattr(_hashlib, 'HASH', None)
+HASHXOF = getattr(_hashlib, 'HASHXOF', None)
+openssl_md_meth_names = getattr(_hashlib, 'openssl_md_meth_names', frozenset())
+get_fips_mode = getattr(_hashlib, 'get_fips_mode', None)
+if not get_fips_mode:
     def get_fips_mode():
         return 0
 
@@ -566,9 +569,14 @@ def check_sha3(self, name, capacity, rate, suffix):
         constructors = self.constructors_to_test[name]
         for hash_object_constructor in constructors:
             m = hash_object_constructor()
-            if HASH is not None and isinstance(m, HASH):
-                # _hashopenssl's variant does not have extra SHA3 attributes
-                continue
+            if name.startswith('shake_'):
+                if HASHXOF is not None and isinstance(m, HASHXOF):
+                    # _hashopenssl's variant does not have extra SHA3 attributes
+                    continue
+            else:
+                if HASH is not None and isinstance(m, HASH):
+                    # _hashopenssl's variant does not have extra SHA3 attributes
+                    continue
             self.assertEqual(capacity + rate, 1600)
             self.assertEqual(m._capacity_bits, capacity)
             self.assertEqual(m._rate_bits, rate)
@@ -1070,7 +1078,8 @@ def test_disallow_instantiation(self):
     def test_hash_disallow_instantiation(self):
         # internal types like _hashlib.HASH are not constructable
         support.check_disallow_instantiation(self, HASH)
-        support.check_disallow_instantiation(self, HASHXOF)
+        if HASHXOF is not None:
+            support.check_disallow_instantiation(self, HASHXOF)
 
     def test_readonly_types(self):
         for algorithm, constructors in self.constructors_to_test.items():