diff --git a/CHANGES b/CHANGES
index 4198395c61b..5d5a2b2b353 100644
--- a/CHANGES
+++ b/CHANGES
@@ -18,6 +18,7 @@ Bugs fixed
 
 * #7808: autodoc: Warnings raised on variable and attribute type annotations
 * #7802: autodoc: EOFError is raised on parallel build
+* #7821: autodoc: TypeError is raised for overloaded C-ext function
 * #7812: autosummary: generates broken stub files if the target code contains
   an attribute and module that are same name
 * #7811: sphinx.util.inspect causes circular import problem
diff --git a/sphinx/ext/autodoc/__init__.py b/sphinx/ext/autodoc/__init__.py
index 64b56847b37..754c4fddaf2 100644
--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -1237,7 +1237,11 @@ def annotate_to_first_argument(self, func: Callable, typ: Type) -> None:
         params = list(sig.parameters.values())
         if params[0].annotation is Parameter.empty:
             params[0] = params[0].replace(annotation=typ)
-            func.__signature__ = sig.replace(parameters=params)  # type: ignore
+            try:
+                func.__signature__ = sig.replace(parameters=params)  # type: ignore
+            except TypeError:
+                # failed to update signature (ex. built-in or extension types)
+                return
 
 
 class SingledispatchFunctionDocumenter(FunctionDocumenter):
@@ -1833,7 +1837,11 @@ def annotate_to_first_argument(self, func: Callable, typ: Type) -> None:
         params = list(sig.parameters.values())
         if params[1].annotation is Parameter.empty:
             params[1] = params[1].replace(annotation=typ)
-            func.__signature__ = sig.replace(parameters=params)  # type: ignore
+            try:
+                func.__signature__ = sig.replace(parameters=params)  # type: ignore
+            except TypeError:
+                # failed to update signature (ex. built-in or extension types)
+                return
 
 
 class SingledispatchMethodDocumenter(MethodDocumenter):