diff --git a/include/pybind11/detail/common.h b/include/pybind11/detail/common.h
index 1032293d21..129039252f 100644
--- a/include/pybind11/detail/common.h
+++ b/include/pybind11/detail/common.h
@@ -754,7 +754,16 @@ template <typename C, typename R, typename... A>
 struct remove_class<R (C::*)(A...) const> {
     using type = R(A...);
 };
-
+#ifdef __cpp_noexcept_function_type
+template <typename C, typename R, typename... A>
+struct remove_class<R (C::*)(A...) noexcept> {
+    using type = R(A...);
+};
+template <typename C, typename R, typename... A>
+struct remove_class<R (C::*)(A...) const noexcept> {
+    using type = R(A...);
+};
+#endif
 /// Helper template to strip away type modifiers
 template <typename T>
 struct intrinsic_type {
diff --git a/tests/test_constants_and_functions.cpp b/tests/test_constants_and_functions.cpp
index 922375c5ea..312edca9e0 100644
--- a/tests/test_constants_and_functions.cpp
+++ b/tests/test_constants_and_functions.cpp
@@ -148,4 +148,7 @@ TEST_SUBMODULE(constants_and_functions, m) {
             py::arg_v("y", 42, "<the answer>"),
             py::arg_v("z", default_value));
     });
+
+    // test noexcept(true) lambda (#4565)
+    m.def("l1", []() noexcept(true) { return 0; });
 }
diff --git a/tests/test_constants_and_functions.py b/tests/test_constants_and_functions.py
index 5da0b84b8e..a1142461c0 100644
--- a/tests/test_constants_and_functions.py
+++ b/tests/test_constants_and_functions.py
@@ -50,3 +50,7 @@ def __repr__(self):
         m.register_large_capture_with_invalid_arguments(m)
     with pytest.raises(RuntimeError):
         m.register_with_raising_repr(m, RaisingRepr())
+
+
+def test_noexcept_lambda():
+    assert m.l1() == 0