diff --git a/Lib/test/test_hashlib.py b/Lib/test/test_hashlib.py
index 489bb049d2fadb..f0e2d527af2615 100644
--- a/Lib/test/test_hashlib.py
+++ b/Lib/test/test_hashlib.py
@@ -134,8 +134,11 @@ def __init__(self, *args, **kwargs):
             algorithms.add(algorithm.lower())
 
         _blake2 = self._conditional_import_module('_blake2')
+        blake2_hashes = {'blake2b', 'blake2s'}
         if _blake2:
-            algorithms.update({'blake2b', 'blake2s'})
+            algorithms.update(blake2_hashes)
+        else:
+            algorithms.difference_update(blake2_hashes)
 
         self.constructors_to_test = {}
         for algorithm in algorithms:
@@ -232,7 +235,12 @@ def test_algorithms_available(self):
         # all available algorithms must be loadable, bpo-47101
         self.assertNotIn("undefined", hashlib.algorithms_available)
         for name in hashlib.algorithms_available:
-            digest = hashlib.new(name, usedforsecurity=False)
+            with self.subTest(name):
+                try:
+                    _ = hashlib.new(name, usedforsecurity=False)
+                except ValueError as exc:
+                    self.skip_if_blake2_not_builtin(name, exc)
+                    raise
 
     def test_usedforsecurity_true(self):
         hashlib.new("sha256", usedforsecurity=True)
@@ -504,6 +512,7 @@ def test_sha3_256_update_over_4gb(self):
         self.assertEqual(h.hexdigest(), "e2d4535e3b613135c14f2fe4e026d7ad8d569db44901740beffa30d430acb038")
 
     @requires_resource('cpu')
+    @requires_blake2
     def test_blake2_update_over_4gb(self):
         # blake2s or blake2b doesn't matter based on how our C code is structured, this tests the
         # common loop macro logic.
@@ -798,6 +807,12 @@ def test_case_sha512_3(self):
           "e718483d0ce769644e2e42c7bc15b4638e1f98b13b2044285632a803afa973eb"+
           "de0ff244877ea60a4cb0432ce577c31beb009c5c2c49aa2e4eadb217ad8cc09b")
 
+    def skip_if_blake2_not_builtin(self, name, skip_reason):
+        # blake2 builtins may be absent if python built with
+        # a subset of --with-builtin-hashlib-hashes or none.
+        if "blake2" in name and "blake2" not in builtin_hashes:
+            self.skipTest(skip_reason)
+
     def check_blake2(self, constructor, salt_size, person_size, key_size,
                      digest_size, max_offset):
         self.assertEqual(constructor.SALT_SIZE, salt_size)
@@ -1080,10 +1095,16 @@ def test_sha256_gil(self):
     def test_threaded_hashing_fast(self):
         # Same as test_threaded_hashing_slow() but only tests some functions
         # since otherwise test_hashlib.py becomes too slow during development.
-        for name in ['md5', 'sha1', 'sha256', 'sha3_256', 'blake2s']:
+        algos = ['md5', 'sha1', 'sha256', 'sha3_256', 'blake2s']
+        for name in algos:
             if constructor := getattr(hashlib, name, None):
                 with self.subTest(name):
-                    self.do_test_threaded_hashing(constructor, is_shake=False)
+                    try:
+                        self.do_test_threaded_hashing(constructor, is_shake=False)
+                    except ValueError as exc:
+                        self.skip_if_blake2_not_builtin(name, exc)
+                        raise
+
         if shake_128 := getattr(hashlib, 'shake_128', None):
             self.do_test_threaded_hashing(shake_128, is_shake=True)