diff --git a/mypy/semanal.py b/mypy/semanal.py
index 5ef5223c2346..4a45032528e9 100644
--- a/mypy/semanal.py
+++ b/mypy/semanal.py
@@ -1902,7 +1902,11 @@ def analyze_type_param(
     ) -> TypeVarLikeExpr | None:
         fullname = self.qualified_name(type_param.name)
         if type_param.upper_bound:
-            upper_bound = self.anal_type(type_param.upper_bound, allow_placeholder=True)
+            upper_bound = self.anal_type(
+                type_param.upper_bound,
+                allow_placeholder=True,
+                prohibit_self_type="type parameter bound",
+            )
             # TODO: we should validate the upper bound is valid for a given kind.
             if upper_bound is None:
                 # This and below copies special-casing for old-style type variables, that
@@ -1926,6 +1930,7 @@ def analyze_type_param(
                 allow_tuple_literal=type_param.kind == PARAM_SPEC_KIND,
                 allow_unpack=type_param.kind == TYPE_VAR_TUPLE_KIND,
                 analyzing_tvar_def=True,
+                prohibit_self_type="type parameter default",
             )
             if default is None:
                 default = PlaceholderType(None, [], context.line)
@@ -1943,7 +1948,11 @@ def analyze_type_param(
             values: list[Type] = []
             if type_param.values:
                 for value in type_param.values:
-                    analyzed = self.anal_type(value, allow_placeholder=True)
+                    analyzed = self.anal_type(
+                        value,
+                        allow_placeholder=True,
+                        prohibit_self_type="type parameter constraint",
+                    )
                     if analyzed is None:
                         analyzed = PlaceholderType(None, [], context.line)
                     if has_type_vars(analyzed):
diff --git a/test-data/unit/check-selftype.test b/test-data/unit/check-selftype.test
index 6f73df5e05c8..947a7181078c 100644
--- a/test-data/unit/check-selftype.test
+++ b/test-data/unit/check-selftype.test
@@ -1494,6 +1494,23 @@ def func() -> None:
 
 class C(Self): ...  # E: Self type is only allowed in annotations within class definition
 
+[case testTypingSelfInvalidTypeParamPositions]
+# https://github.com/python/mypy/issues/21960
+# flags: --python-version 3.13
+from typing import Self
+
+class Foo:
+    def meth[T: Self](self: T) -> None: ...  # E: Self type cannot be used in type parameter bound
+
+class Bar[T: Self]: ...  # E: Self type cannot be used in type parameter bound
+
+def func[T: (Self, int)](x: T) -> None: ...  # E: Self type cannot be used in type parameter constraint
+
+type Alias[T: Self] = list[T]  # E: Self type cannot be used in type parameter bound
+
+class Ok[T]:
+    def meth(self: Self) -> None: ...
+
 [case testTypingSelfInvalidArgs]
 from typing import Self, List