diff --git a/changelog/879.bugfix.rst b/changelog/879.bugfix.rst
new file mode 100644
index 00000000..d2ebf007
--- /dev/null
+++ b/changelog/879.bugfix.rst
@@ -0,0 +1 @@
+Improve detection of disabled BLAKE2 hashing due to FIPS mode.
diff --git a/tests/test_package.py b/tests/test_package.py
index 3d2e2799..609c95ea 100644
--- a/tests/test_package.py
+++ b/tests/test_package.py
@@ -307,9 +307,10 @@ def test_fips_hash_manager_md5(monkeypatch):
     assert hasher.hexdigest() == hashes
 
 
-def test_fips_hash_manager_blake2(monkeypatch):
+@pytest.mark.parametrize("exception_class", [TypeError, ValueError])
+def test_fips_hash_manager_blake2(exception_class, monkeypatch):
     """Generate hexdigest without BLAKE2 when hashlib is using FIPS mode."""
-    replaced_blake2b = pretend.raiser(ValueError("fipsmode"))
+    replaced_blake2b = pretend.raiser(exception_class("fipsmode"))
     monkeypatch.setattr(package_file.hashlib, "blake2b", replaced_blake2b)
 
     filename = "tests/fixtures/twine-1.5.0-py2.py3-none-any.whl"
diff --git a/twine/package.py b/twine/package.py
index 168f9665..3ca074fe 100644
--- a/twine/package.py
+++ b/twine/package.py
@@ -268,7 +268,7 @@ def __init__(self, filename: str) -> None:
         self._blake_hasher = None
         try:
             self._blake_hasher = hashlib.blake2b(digest_size=256 // 8)
-        except ValueError:
+        except (ValueError, TypeError):
             # FIPS mode disables blake2
             pass