diff --git a/src/poetry/repositories/http_repository.py b/src/poetry/repositories/http_repository.py
index 515907e72e5..6c000ac981f 100644
--- a/src/poetry/repositories/http_repository.py
+++ b/src/poetry/repositories/http_repository.py
@@ -4,6 +4,7 @@
 import hashlib
 
 from contextlib import contextmanager
+from contextlib import suppress
 from pathlib import Path
 from typing import TYPE_CHECKING
 from typing import Any
@@ -374,7 +375,11 @@ def calculate_sha256(self, link: Link) -> str | None:
             hash_name = get_highest_priority_hash_type(
                 set(link.hashes.keys()), link.filename
             )
-            known_hash = getattr(hashlib, hash_name)() if hash_name else None
+            known_hash = None
+            with suppress(ValueError, AttributeError):
+                # Handle ValueError here as well since under FIPS environments
+                # this is what is raised (e.g., for MD5)
+                known_hash = getattr(hashlib, hash_name)() if hash_name else None
             required_hash = hashlib.sha256()
 
             chunksize = 4096
diff --git a/tests/repositories/test_http_repository.py b/tests/repositories/test_http_repository.py
index 20475bc2c3a..6d7fd667b02 100644
--- a/tests/repositories/test_http_repository.py
+++ b/tests/repositories/test_http_repository.py
@@ -171,3 +171,71 @@ def test_get_info_from_wheel_state_sequence(mocker: MockerFixture) -> None:
 
     assert mock_metadata_from_wheel_url.call_count == 5
     assert mock_download.call_count == 4
+
+
+@pytest.mark.parametrize(
+    "mock_hashes",
+    [
+        None,
+        {"sha256": "e216b70f013c47b82a72540d34347632c5bfe59fd54f5fe5d51f6a68b19aaf84"},
+        {"md5": "be7589b4902793e66d7d979bd8581591"},
+    ],
+)
+def test_calculate_sha256(
+    mocker: MockerFixture, mock_hashes: dict[str, Any] | None
+) -> None:
+    filename = "poetry_core-1.5.0-py3-none-any.whl"
+    filepath = MockRepository.DIST_FIXTURES / filename
+    mock_download = mocker.patch(
+        "poetry.repositories.http_repository.download_file",
+        side_effect=lambda _, dest, *args, **kwargs: shutil.copy(filepath, dest),
+    )
+    domain = "foo.com"
+    link = Link(f"https://{domain}/{filename}", hashes=mock_hashes)
+    repo = MockRepository()
+
+    calculated_hash = repo.calculate_sha256(link)
+
+    assert mock_download.call_count == 1
+    assert (
+        calculated_hash
+        == "sha256:e216b70f013c47b82a72540d34347632c5bfe59fd54f5fe5d51f6a68b19aaf84"
+    )
+
+
+def test_calculate_sha256_defaults_to_sha256_on_md5_errors(
+    mocker: MockerFixture,
+) -> None:
+    raised_value_error = False
+
+    def mock_hashlib_md5_error() -> None:
+        nonlocal raised_value_error
+        raised_value_error = True
+        raise ValueError(
+            "[digital envelope routines: EVP_DigestInit_ex] disabled for FIPS"
+        )
+
+    filename = "poetry_core-1.5.0-py3-none-any.whl"
+    filepath = MockRepository.DIST_FIXTURES / filename
+    mock_download = mocker.patch(
+        "poetry.repositories.http_repository.download_file",
+        side_effect=lambda _, dest, *args, **kwargs: shutil.copy(filepath, dest),
+    )
+    mock_hashlib_md5 = mocker.patch("hashlib.md5", side_effect=mock_hashlib_md5_error)
+
+    domain = "foo.com"
+    link = Link(
+        f"https://{domain}/{filename}",
+        hashes={"md5": "be7589b4902793e66d7d979bd8581591"},
+    )
+    repo = MockRepository()
+
+    calculated_hash = repo.calculate_sha256(link)
+
+    assert raised_value_error
+    assert mock_download.call_count == 1
+    assert mock_hashlib_md5.call_count == 1
+    assert (
+        calculated_hash
+        == "sha256:e216b70f013c47b82a72540d34347632c5bfe59fd54f5fe5d51f6a68b19aaf84"
+    )