diff --git a/sphinx/domains/python.py b/sphinx/domains/python.py
index 930f8e72f21..ec440bd40ca 100644
--- a/sphinx/domains/python.py
+++ b/sphinx/domains/python.py
@@ -51,7 +51,7 @@
 py_sig_re = re.compile(
     r'''^ ([\w.]*\.)?            # class name(s)
           (\w+)  \s*             # thing name
-          (?: \[\s*(.*)\s*])?    # optional: type parameters list
+          (?: \[\s*(.*?)\s*\])?  # optional: type parameters list
           (?: \(\s*(.*)\s*\)     # optional: arguments
            (?:\s* -> \s* (.*))?  #           return annotation
           )? $                   # and nothing more
diff --git a/tests/test_domain_py.py b/tests/test_domain_py.py
index c5a044bc663..a9793b6788d 100644
--- a/tests/test_domain_py.py
+++ b/tests/test_domain_py.py
@@ -59,6 +59,12 @@ def test_function_signatures():
     rv = parse('func(a=1) -> int object')
     assert rv == '(a=1)'
 
+    rv = parse('func[Annotated[typename]](a=1) -> int')
+    assert rv == '(a=1)'
+
+    rv = parse('func[Annotated[typename]](a=1) -> Annotated[typename]')
+    assert rv == '(a=1)'
+
     rv = parse('func(a=1, [b=None])')
     assert rv == '(a=1, [b=None])'