diff --git a/changelog/776.bugfix.rst b/changelog/776.bugfix.rst
new file mode 100644
index 00000000..222d4b67
--- /dev/null
+++ b/changelog/776.bugfix.rst
@@ -0,0 +1,3 @@
+Do not include md5_digest or blake2_256_digest if FIPS mode is enabled on the
+host. This removes those fields from the metadata before sending the metadata
+to the repository.
diff --git a/tests/test_package.py b/tests/test_package.py
index 45cc420b..0e261f0f 100644
--- a/tests/test_package.py
+++ b/tests/test_package.py
@@ -262,6 +262,24 @@ def test_fips_hash_manager_blake2(monkeypatch):
     assert hasher.hexdigest() == hashes
 
 
+def test_fips_packagefile(monkeypatch):
+    """Generate a metadata dictionary when FIPS is enabled.
+
+    See also: https://github.com/pypa/twine/issues/775
+    """
+    replaced_blake2b = pretend.raiser(ValueError("fipsmode"))
+    replaced_md5 = pretend.raiser(ValueError("fipsmode"))
+    monkeypatch.setattr(package_file.hashlib, "md5", replaced_md5)
+    monkeypatch.setattr(package_file.hashlib, "blake2b", replaced_blake2b)
+
+    filename = "tests/fixtures/twine-1.5.0-py2.py3-none-any.whl"
+    pf = package_file.PackageFile.from_filename(filename, None)
+
+    mddict = pf.metadata_dictionary()
+    assert "md5_digest" not in mddict
+    assert "blake2_256_digest" not in mddict
+
+
 def test_pkginfo_returns_no_metadata(monkeypatch):
     """Raise an exception when pkginfo can't interpret the metadata.
 
diff --git a/twine/package.py b/twine/package.py
index a2da7612..22c05944 100644
--- a/twine/package.py
+++ b/twine/package.py
@@ -152,9 +152,7 @@ def metadata_dictionary(self) -> Dict[str, MetadataValue]:
             "download_url": meta.download_url,
             "supported_platform": meta.supported_platforms,
             "comment": self.comment,
-            "md5_digest": self.md5_digest,
             "sha256_digest": self.sha2_digest,
-            "blake2_256_digest": self.blake2_256_digest,
             # PEP 314
             "provides": meta.provides,
             "requires": meta.requires,
@@ -174,6 +172,14 @@ def metadata_dictionary(self) -> Dict[str, MetadataValue]:
         if self.gpg_signature is not None:
             data["gpg_signature"] = self.gpg_signature
 
+        # FIPS will make us send None/null to a package repository and some of
+        # them don't appreciate that. FIPS disables both MD5 and Blake2
+        if self.md5_digest:
+            data["md5_digest"] = self.md5_digest
+
+        if self.blake2_256_digest:
+            data["blake2_256_digest"] = self.blake2_256_digest
+
         return data
 
     def add_gpg_signature(