diff --git a/mypy/stubgenc.py b/mypy/stubgenc.py
index d86818adf2a4..e7aa670c4f15 100755
--- a/mypy/stubgenc.py
+++ b/mypy/stubgenc.py
@@ -13,7 +13,7 @@
 import keyword
 import os.path
 from collections.abc import Callable, Mapping
-from types import FunctionType, ModuleType
+from types import FunctionType, ModuleType, UnionType
 from typing import Any
 
 from mypy.fastparse import parse_type_comment
@@ -768,10 +768,16 @@ def generate_property_stub(
 
                 rw_properties.append(f"{self._indent}{name}: {inferred_type}")
 
-    def get_type_fullname(self, typ: type) -> str:
+    def get_type_fullname(self, typ: type | UnionType) -> str:
         """Given a type, return a string representation"""
         if typ is Any:
             return "Any"
+        if isinstance(typ, UnionType):
+            # PEP 604 unions (``X | Y``) have no ``__name__`` / ``__qualname__``.
+            return " | ".join(
+                "None" if arg is type(None) else self.get_type_fullname(arg)
+                for arg in typ.__args__
+            )
         typename = getattr(typ, "__qualname__", typ.__name__)
         module_name = self.get_obj_module(typ)
         if module_name is None:
diff --git a/test-data/unit/stubgen.test b/test-data/unit/stubgen.test
index 0c8b74ecf29a..0f583b2c6d50 100644
--- a/test-data/unit/stubgen.test
+++ b/test-data/unit/stubgen.test
@@ -55,6 +55,11 @@ def f(x='foo'): ...
 [out]
 def f(x: str = ...): ...
 
+[case testInspectUnionType_inspect]
+def f(x: int | str) -> float | None: ...
+[out]
+def f(x: int | str) -> float | None: ...
+
 [case testDefaultArgBytes]
 def f(x=b'foo',y=b"what's up",z=b'\xc3\xa0 la une'): ...
 [out]