diff --git a/mypy/typeanal.py b/mypy/typeanal.py
index 31dac8b24e146..4b3278049fdbc 100644
--- a/mypy/typeanal.py
+++ b/mypy/typeanal.py
@@ -1026,8 +1026,10 @@ def analyze_callable_args_for_paramspec(
     def analyze_callable_args_for_concatenate(
         self, callable_args: Type, ret_type: Type, fallback: Instance
     ) -> CallableType | None:
-        """Construct a 'Callable[C, RET]', where C is Concatenate[..., P], returning None if we
-        cannot.
+        """Construct a 'Callable[C, RET]', where C is Concatenate[..., P]
+
+        Return `None` if we cannot.
+        Return `AnyType` if we only can do it partially.
         """
         if not isinstance(callable_args, UnboundType):
             return None
@@ -1039,7 +1041,17 @@ def analyze_callable_args_for_concatenate(
         if sym.node.fullname not in ("typing_extensions.Concatenate", "typing.Concatenate"):
             return None
 
-        tvar_def = self.anal_type(callable_args, allow_param_spec=True)
+        tvar_def = get_proper_type(self.anal_type(callable_args, allow_param_spec=True))
+        if isinstance(tvar_def, AnyType) and tvar_def.type_of_any == TypeOfAny.from_error:
+            # Some error happened, we won't be able to construct a proper type anyway.
+            # So, instead return a callable that accepts anything.
+            return CallableType(
+                arg_names=[None] * 2,
+                arg_types=[AnyType(TypeOfAny.from_error)] * 2,
+                arg_kinds=[ARG_STAR, ARG_STAR2],
+                ret_type=AnyType(TypeOfAny.from_error),
+                fallback=fallback,
+            )
         if not isinstance(tvar_def, ParamSpecType):
             return None
 
diff --git a/test-data/unit/check-parameter-specification.test b/test-data/unit/check-parameter-specification.test
index a561acba693c7..4da2a55eebd0d 100644
--- a/test-data/unit/check-parameter-specification.test
+++ b/test-data/unit/check-parameter-specification.test
@@ -680,6 +680,17 @@ def f(x: int) -> None: ...
 n.foo(f)
 [builtins fixtures/paramspec.pyi]
 
+[case testLastParameterToConcatenateAndInvalidCallable]
+# See https://github.com/python/mypy/issues/13518
+from typing_extensions import Concatenate, ParamSpec
+from typing import Callable, TypeVar, Any
+
+P = ParamSpec("P")
+
+def f(fn: Callable[Concatenate[P, int], None]): ...  # E: The last parameter to Concatenate needs to be a ParamSpec
+reveal_type(f)  # N: Revealed type is "def [P] (fn: def (*Any, **Any) -> Any) -> Any"
+[builtins fixtures/paramspec.pyi]
+
 [case testParamSpecLiteralsTypeApplication]
 from typing_extensions import ParamSpec
 from typing import Generic, Callable