diff --git a/news/12579.bugfix.rst b/news/12579.bugfix.rst
new file mode 100644
index 00000000000..df189e8fbff
--- /dev/null
+++ b/news/12579.bugfix.rst
@@ -0,0 +1 @@
+Remove duplication in invalid wheel error message
diff --git a/src/pip/_internal/metadata/importlib/_dists.py b/src/pip/_internal/metadata/importlib/_dists.py
index 26370facf28..8591029f16e 100644
--- a/src/pip/_internal/metadata/importlib/_dists.py
+++ b/src/pip/_internal/metadata/importlib/_dists.py
@@ -133,8 +133,6 @@ def from_wheel(cls, wheel: Wheel, name: str) -> BaseDistribution:
                 dist = WheelDistribution.from_zipfile(zf, name, wheel.location)
         except zipfile.BadZipFile as e:
             raise InvalidWheel(wheel.location, name) from e
-        except UnsupportedWheel as e:
-            raise UnsupportedWheel(f"{name} has an invalid wheel, {e}")
         return cls(dist, dist.info_location, pathlib.PurePosixPath(wheel.location))
 
     @property
diff --git a/src/pip/_internal/utils/wheel.py b/src/pip/_internal/utils/wheel.py
index 3551f8f19bc..f85aee8a3f9 100644
--- a/src/pip/_internal/utils/wheel.py
+++ b/src/pip/_internal/utils/wheel.py
@@ -28,7 +28,7 @@ def parse_wheel(wheel_zip: ZipFile, name: str) -> Tuple[str, Message]:
         metadata = wheel_metadata(wheel_zip, info_dir)
         version = wheel_version(metadata)
     except UnsupportedWheel as e:
-        raise UnsupportedWheel(f"{name} has an invalid wheel, {str(e)}")
+        raise UnsupportedWheel(f"{name} has an invalid wheel, {e}")
 
     check_compatibility(version, name)