diff --git a/docs/changelog.rst b/docs/changelog.rst
index 2272a37e..afc4c74e 100644
--- a/docs/changelog.rst
+++ b/docs/changelog.rst
@@ -25,6 +25,9 @@ Upcoming version (TBA)
   long-standing inconvenience. (PR `#778
   <https://github.com/wjakob/nanobind/pull/778>`__).
 
+- The type caster for ``std::function`` now properly identifies its type as
+  optional (the runtime behavior is unaffected; this only impacts stubs)
+
 * ABI version 16.
 
 
diff --git a/include/nanobind/stl/function.h b/include/nanobind/stl/function.h
index b9623402..3a6b0a2f 100644
--- a/include/nanobind/stl/function.h
+++ b/include/nanobind/stl/function.h
@@ -50,9 +50,9 @@ struct type_caster<std::function<Return(Args...)>> {
         std::conditional_t<std::is_void_v<Return>, void_type, Return>>;
 
     NB_TYPE_CASTER(std::function <Return(Args...)>,
-                   const_name(NB_TYPING_CALLABLE "[[") +
+                   optional_name(const_name(NB_TYPING_CALLABLE "[[") +
                        concat(make_caster<Args>::Name...) + const_name("], ") +
-                       ReturnCaster::Name + const_name("]"))
+                       ReturnCaster::Name + const_name("]")))
 
     struct pyfunc_wrapper_t : pyfunc_wrapper {
         using pyfunc_wrapper::pyfunc_wrapper;
diff --git a/tests/test_functions_ext.pyi.ref b/tests/test_functions_ext.pyi.ref
index 3f29c604..5cc64208 100644
--- a/tests/test_functions_ext.pyi.ref
+++ b/tests/test_functions_ext.pyi.ref
@@ -182,7 +182,7 @@ def test_bytearray_resize(arg0: bytearray, arg1: int, /) -> None: ...
 
 def test_bytearray_size(arg: bytearray, /) -> int: ...
 
-def test_call_1(arg: Callable[[int], int], /) -> object: ...
+def test_call_1(arg: Callable[[int], int] | None, /) -> object: ...
 
 def test_call_2(arg: Callable[[int, int], None], /) -> object: ...
 
diff --git a/tests/test_stl_ext.pyi.ref b/tests/test_stl_ext.pyi.ref
index ac8f39f8..25a21feb 100644
--- a/tests/test_stl_ext.pyi.ref
+++ b/tests/test_stl_ext.pyi.ref
@@ -38,10 +38,10 @@ class FuncWrapper:
     def __init__(self) -> None: ...
 
     @property
-    def f(self) -> Callable[[], None]: ...
+    def f(self) -> Callable[[], None] | None: ...
 
     @f.setter
-    def f(self, arg: Callable[[], None], /) -> None: ...
+    def f(self, arg: Callable[[], None] | None, /) -> None: ...
 
     alive: int = ...
     """static read-only property"""
@@ -87,7 +87,7 @@ def array_in(arg: Sequence[int], /) -> int: ...
 
 def array_out() -> list[int]: ...
 
-def call_function(arg0: Callable[[int], int], arg1: int, /) -> int: ...
+def call_function(arg0: Callable[[int], int] | None, arg1: int, /) -> int: ...
 
 def complex_array_double(arg: Sequence[complex], /) -> list[complex]: ...
 
@@ -182,15 +182,15 @@ def return_copyable() -> Copyable: ...
 
 def return_copyable_ptr() -> Copyable: ...
 
-def return_empty_function() -> Callable[[int], int]: ...
+def return_empty_function() -> Callable[[int], int] | None: ...
 
-def return_function() -> Callable[[int], int]: ...
+def return_function() -> Callable[[int], int] | None: ...
 
 def return_movable() -> Movable: ...
 
 def return_movable_ptr() -> Movable: ...
 
-def return_void_function(arg: Callable[[], None], /) -> Callable[[], None]: ...
+def return_void_function(arg: Callable[[], None] | None, /) -> Callable[[], None] | None: ...
 
 def set_in_lvalue_ref(x: Set[str]) -> None: ...