diff --git a/src/pip/_internal/network/lazy_wheel.py b/src/pip/_internal/network/lazy_wheel.py
index 758cc174b85..f5520b4565c 100644
--- a/src/pip/_internal/network/lazy_wheel.py
+++ b/src/pip/_internal/network/lazy_wheel.py
@@ -18,7 +18,7 @@
 from pip._vendor.requests.models import CONTENT_CHUNK_SIZE, HTTPError, Response
 from pip._vendor.requests.status_codes import codes
 
-from pip._internal.exceptions import InvalidWheel
+from pip._internal.exceptions import InvalidWheel, UnsupportedWheel
 from pip._internal.metadata import BaseDistribution, MemoryWheel, get_wheel_distribution
 from pip._internal.network.session import PipSession as Session
 from pip._internal.network.utils import HEADERS
@@ -47,7 +47,7 @@ def dist_from_wheel_url(name: str, url: str, session: Session) -> BaseDistributi
             wheel = MemoryWheel(zf.name, zf)
             # After context manager exit, wheel.name is an invalid file by intention.
             return get_wheel_distribution(wheel, canonicalize_name(name))
-    except BadZipFile:
+    except (BadZipFile, UnsupportedWheel):
         raise InvalidWheel(url, name)