diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index bd0ee273..5689d5a3 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -950,6 +950,9 @@ public:
     static_assert(detail::all_of<is_valid_class_option<options>...>::value,
             "Unknown/invalid class_ template parameters provided");
 
+    static_assert(!has_alias || std::is_polymorphic<type>::value,
+            "Cannot use an alias class with a non-polymorphic type");
+
     PYBIND11_OBJECT(class_, generic_type, PyType_Check)
 
     template <typename... Extra>
diff --git a/tests/test_class.cpp b/tests/test_class.cpp
index 5860b741..670949f8 100644
--- a/tests/test_class.cpp
+++ b/tests/test_class.cpp
@@ -231,7 +231,7 @@ TEST_SUBMODULE(class_, m) {
     bind_local<LocalExternal, 17>(m, "LocalExternal", py::module_local());
 }
 
-template <int N> class BreaksBase {};
+template <int N> class BreaksBase { public: virtual ~BreaksBase() = default; };
 template <int N> class BreaksTramp : public BreaksBase<N> {};
 // These should all compile just fine:
 typedef py::class_<BreaksBase<1>, std::unique_ptr<BreaksBase<1>>, BreaksTramp<1>> DoesntBreak1;