diff --git a/news/12918.removal.rst b/news/12918.removal.rst
new file mode 100644
index 00000000000..c5a52cf66e1
--- /dev/null
+++ b/news/12918.removal.rst
@@ -0,0 +1 @@
+Deprecate wheel filenames that are not compliant with PEP 440.
diff --git a/src/pip/_internal/models/wheel.py b/src/pip/_internal/models/wheel.py
index 36d4d2e785c..63db978f1f5 100644
--- a/src/pip/_internal/models/wheel.py
+++ b/src/pip/_internal/models/wheel.py
@@ -8,6 +8,7 @@
 from pip._vendor.packaging.tags import Tag
 
 from pip._internal.exceptions import InvalidWheelFilename
+from pip._internal.utils.deprecation import deprecated
 
 
 class Wheel:
@@ -29,9 +30,25 @@ def __init__(self, filename: str) -> None:
             raise InvalidWheelFilename(f"{filename} is not a valid wheel filename.")
         self.filename = filename
         self.name = wheel_info.group("name").replace("_", "-")
-        # we'll assume "_" means "-" due to wheel naming scheme
-        # (https://github.com/pypa/pip/issues/1150)
-        self.version = wheel_info.group("ver").replace("_", "-")
+        _version = wheel_info.group("ver")
+        if "_" in _version:
+            deprecated(
+                reason=(
+                    f"Wheel filename {filename!r} uses an invalid filename format, "
+                    f"as the version part {_version!r} is not correctly normalised, "
+                    "and contains an underscore character. Future versions of pip may "
+                    "fail to recognise this wheel."
+                ),
+                replacement=(
+                    "rename the wheel to use a correctly normalised version part "
+                    "(this may require updating the version in the project metadata)"
+                ),
+                gone_in="25.1",
+                issue=12914,
+            )
+            _version = _version.replace("_", "-")
+
+        self.version = _version
         self.build_tag = wheel_info.group("build")
         self.pyversions = wheel_info.group("pyver").split(".")
         self.abis = wheel_info.group("abi").split(".")
diff --git a/tests/unit/test_models_wheel.py b/tests/unit/test_models_wheel.py
index c06525e089e..ee4d88c744a 100644
--- a/tests/unit/test_models_wheel.py
+++ b/tests/unit/test_models_wheel.py
@@ -3,7 +3,7 @@
 
 from pip._internal.exceptions import InvalidWheelFilename
 from pip._internal.models.wheel import Wheel
-from pip._internal.utils import compatibility_tags
+from pip._internal.utils import compatibility_tags, deprecation
 
 
 class TestWheelFile:
@@ -175,5 +175,6 @@ def test_version_underscore_conversion(self) -> None:
         Test that we convert '_' to '-' for versions parsed out of wheel
         filenames
         """
-        w = Wheel("simple-0.1_1-py2-none-any.whl")
+        with pytest.warns(deprecation.PipDeprecationWarning):
+            w = Wheel("simple-0.1_1-py2-none-any.whl")
         assert w.version == "0.1-1"