diff --git a/stdlib/@tests/stubtest_allowlists/py313.txt b/stdlib/@tests/stubtest_allowlists/py313.txt
@@ -1,7 +1,8 @@
 # =========================
 # New errors in Python 3.13
 # =========================
-
+# No way to express keyword-only ParamSpec
+copy.replace
 # ====================================
 # Pre-existing errors from Python 3.12
 # ====================================

diff --git a/stdlib/@tests/stubtest_allowlists/py314.txt b/stdlib/@tests/stubtest_allowlists/py314.txt
@@ -35,6 +35,8 @@ multiprocessing.process.BaseProcess.__init__
 # Pre-existing errors from Python 3.13
 # ====================================
 
+# No way to express keyword-only ParamSpec
+copy.replace
 
 # =======
 # >= 3.12

diff --git a/stdlib/@tests/stubtest_allowlists/py315.txt b/stdlib/@tests/stubtest_allowlists/py315.txt
@@ -175,6 +175,8 @@ types.MappingProxyType.get
 
 typing_extensions.Protocol  # Super-special typing primitive
 
+copy.replace  # Cannot have keyword-only ParamSpec
+
 
 # =============================================================
 # Allowlist entries that cannot or should not be fixed; >= 3.12

diff --git a/stdlib/@tests/test_cases/check_copy.py b/stdlib/@tests/test_cases/check_copy.py
@@ -10,7 +10,7 @@ class ReplaceableClass:
     def __init__(self, val: int) -> None:
         self.val = val
 
-    def __replace__(self, val: int) -> Self:
+    def __replace__(self, /, *, val: int) -> Self:
         cpy = copy.copy(self)
         cpy.val = val
         return cpy
@@ -29,11 +29,11 @@ class Box(Generic[_T_co]):
     def __init__(self, value: _T_co, /) -> None:
         self.value = value
 
-    def __replace__(self, value: str) -> Box[str]:
+    def __replace__(self, /, *, value: str) -> Box[str]:
         return Box(value)
 
 
 if sys.version_info >= (3, 13):
     box1: Box[int] = Box(42)
-    box2 = copy.replace(box1, val="spam")
+    box2 = copy.replace(box1, value="spam")
     assert_type(box2, Box[str])
diff --git a/stdlib/copy.pyi b/stdlib/copy.pyi
@@ -1,15 +1,17 @@
 import sys
 from typing import Any, Protocol, TypeVar, type_check_only
+from typing_extensions import ParamSpec
 
 __all__ = ["Error", "copy", "deepcopy"]
 
 _T = TypeVar("_T")
 _RT_co = TypeVar("_RT_co", covariant=True)
+_P = ParamSpec("_P")
 
 @type_check_only
-class _SupportsReplace(Protocol[_RT_co]):
+class _SupportsReplace(Protocol[_P, _RT_co]):
     # In reality doesn't support args, but there's no great way to express this.
-    def __replace__(self, /, *_: Any, **changes: Any) -> _RT_co: ...
+    def __replace__(self, /, *_: _P.args, **changes: _P.kwargs) -> _RT_co: ...
 
 # None in CPython but non-None in Jython
 PyStringMap: Any
@@ -20,8 +22,10 @@ def copy(x: _T) -> _T: ...
 
 if sys.version_info >= (3, 13):
     __all__ += ["replace"]
-    # The types accepted by `**changes` match those of `obj.__replace__`.
-    def replace(obj: _SupportsReplace[_RT_co], /, **changes: Any) -> _RT_co: ...
+
+    def replace(
+        obj: _SupportsReplace[_P, _RT_co], /, *_: _P.args, **changes: _P.kwargs  # does not accept positional arguments at runtime
+    ) -> _RT_co: ...
 
 class Error(Exception): ...