diff --git a/news/12953.bugfix.rst b/news/12953.bugfix.rst
new file mode 100644
index 00000000000..f2d0521b20e
--- /dev/null
+++ b/news/12953.bugfix.rst
@@ -0,0 +1 @@
+Display disagnostic error message when already installed package has an invalid requirement.
diff --git a/src/pip/_internal/exceptions.py b/src/pip/_internal/exceptions.py
index 8ceb818a35d..45a876a850d 100644
--- a/src/pip/_internal/exceptions.py
+++ b/src/pip/_internal/exceptions.py
@@ -15,6 +15,8 @@
 from itertools import chain, groupby, repeat
 from typing import TYPE_CHECKING, Dict, Iterator, List, Literal, Optional, Union
 
+from pip._vendor.packaging.requirements import InvalidRequirement
+from pip._vendor.packaging.version import InvalidVersion
 from pip._vendor.rich.console import Console, ConsoleOptions, RenderResult
 from pip._vendor.rich.markup import escape
 from pip._vendor.rich.text import Text
@@ -775,3 +777,33 @@ def __init__(self, *, distribution: "BaseDistribution") -> None:
             ),
             hint_stmt=None,
         )
+
+
+class InvalidInstalledPackage(DiagnosticPipError):
+    reference = "invalid-installed-package"
+
+    def __init__(
+        self,
+        *,
+        dist: "BaseDistribution",
+        invalid_exc: Union[InvalidRequirement, InvalidVersion],
+    ) -> None:
+        installed_location = dist.installed_location
+
+        if isinstance(invalid_exc, InvalidRequirement):
+            invalid_type = "requirement"
+        else:
+            invalid_type = "version"
+
+        super().__init__(
+            message=Text(
+                f"Cannot process installed package {dist} "
+                + (f"in {installed_location!r} " if installed_location else "")
+                + f"because it has an invalid {invalid_type}:\n{invalid_exc.args[0]}"
+            ),
+            context=(
+                "Starting with pip 24.1, packages with invalid "
+                f"{invalid_type}s can not be processed."
+            ),
+            hint_stmt="To proceed this package must be uninstalled.",
+        )
diff --git a/src/pip/_internal/resolution/resolvelib/candidates.py b/src/pip/_internal/resolution/resolvelib/candidates.py
index d30d477be68..6617644fe53 100644
--- a/src/pip/_internal/resolution/resolvelib/candidates.py
+++ b/src/pip/_internal/resolution/resolvelib/candidates.py
@@ -9,6 +9,7 @@
 from pip._internal.exceptions import (
     HashError,
     InstallationSubprocessError,
+    InvalidInstalledPackage,
     MetadataInconsistent,
     MetadataInvalid,
 )
@@ -398,8 +399,12 @@ def format_for_error(self) -> str:
     def iter_dependencies(self, with_requires: bool) -> Iterable[Optional[Requirement]]:
         if not with_requires:
             return
-        for r in self.dist.iter_dependencies():
-            yield from self._factory.make_requirements_from_spec(str(r), self._ireq)
+
+        try:
+            for r in self.dist.iter_dependencies():
+                yield from self._factory.make_requirements_from_spec(str(r), self._ireq)
+        except InvalidRequirement as exc:
+            raise InvalidInstalledPackage(dist=self.dist, invalid_exc=exc) from None
 
     def get_install_requirement(self) -> Optional[InstallRequirement]:
         return None
diff --git a/src/pip/_internal/resolution/resolvelib/factory.py b/src/pip/_internal/resolution/resolvelib/factory.py
index 145bdbf71a1..dc6e2e12e1f 100644
--- a/src/pip/_internal/resolution/resolvelib/factory.py
+++ b/src/pip/_internal/resolution/resolvelib/factory.py
@@ -23,13 +23,14 @@
 from pip._vendor.packaging.requirements import InvalidRequirement
 from pip._vendor.packaging.specifiers import SpecifierSet
 from pip._vendor.packaging.utils import NormalizedName, canonicalize_name
-from pip._vendor.packaging.version import Version
+from pip._vendor.packaging.version import InvalidVersion, Version
 from pip._vendor.resolvelib import ResolutionImpossible
 
 from pip._internal.cache import CacheEntry, WheelCache
 from pip._internal.exceptions import (
     DistributionNotFound,
     InstallationError,
+    InvalidInstalledPackage,
     MetadataInconsistent,
     MetadataInvalid,
     UnsupportedPythonVersion,
@@ -283,10 +284,15 @@ def _get_installed_candidate() -> Optional[Candidate]:
                 installed_dist = self._installed_dists[name]
             except KeyError:
                 return None
-            # Don't use the installed distribution if its version does not fit
-            # the current dependency graph.
-            if not specifier.contains(installed_dist.version, prereleases=True):
-                return None
+
+            try:
+                # Don't use the installed distribution if its version
+                # does not fit the current dependency graph.
+                if not specifier.contains(installed_dist.version, prereleases=True):
+                    return None
+            except InvalidVersion as e:
+                raise InvalidInstalledPackage(dist=installed_dist, invalid_exc=e)
+
             candidate = self._make_candidate_from_dist(
                 dist=installed_dist,
                 extras=extras,