diff --git a/mypy/semanal.py b/mypy/semanal.py
index e0a3db2bff1b..4bf9f0c3eabb 100644
--- a/mypy/semanal.py
+++ b/mypy/semanal.py
@@ -2169,8 +2169,16 @@ def analyze_base_classes(
             if (
                 isinstance(base_expr, RefExpr)
                 and base_expr.fullname in TYPED_NAMEDTUPLE_NAMES + TPDICT_NAMES
+            ) or (
+                isinstance(base_expr, CallExpr)
+                and isinstance(base_expr.callee, RefExpr)
+                and base_expr.callee.fullname in TPDICT_NAMES
             ):
                 # Ignore magic bases for now.
+                # For example:
+                #  class Foo(TypedDict): ...  # RefExpr
+                #  class Foo(NamedTuple): ...  # RefExpr
+                #  class Foo(TypedDict("Foo", {"a": int})): ...  # CallExpr
                 continue
 
             try:
diff --git a/mypy/semanal_typeddict.py b/mypy/semanal_typeddict.py
index 67c05fd74273..dbec981bdc96 100644
--- a/mypy/semanal_typeddict.py
+++ b/mypy/semanal_typeddict.py
@@ -79,6 +79,8 @@ def analyze_typeddict_classdef(self, defn: ClassDef) -> tuple[bool, TypeInfo | N
         """
         possible = False
         for base_expr in defn.base_type_exprs:
+            if isinstance(base_expr, CallExpr):
+                base_expr = base_expr.callee
             if isinstance(base_expr, IndexExpr):
                 base_expr = base_expr.base
             if isinstance(base_expr, RefExpr):
@@ -117,7 +119,13 @@ def analyze_typeddict_classdef(self, defn: ClassDef) -> tuple[bool, TypeInfo | N
         typeddict_bases: list[Expression] = []
         typeddict_bases_set = set()
         for expr in defn.base_type_exprs:
-            if isinstance(expr, RefExpr) and expr.fullname in TPDICT_NAMES:
+            ok, maybe_type_info, _ = self.check_typeddict(expr, None, False)
+            if ok and maybe_type_info is not None:
+                # expr is a CallExpr
+                info = maybe_type_info
+                typeddict_bases_set.add(info.fullname)
+                typeddict_bases.append(expr)
+            elif isinstance(expr, RefExpr) and expr.fullname in TPDICT_NAMES:
                 if "TypedDict" not in typeddict_bases_set:
                     typeddict_bases_set.add("TypedDict")
                 else:
@@ -176,12 +184,11 @@ def add_keys_and_types_from_base(
         required_keys: set[str],
         ctx: Context,
     ) -> None:
+        base_args: list[Type] = []
         if isinstance(base, RefExpr):
             assert isinstance(base.node, TypeInfo)
             info = base.node
-            base_args: list[Type] = []
-        else:
-            assert isinstance(base, IndexExpr)
+        elif isinstance(base, IndexExpr):
             assert isinstance(base.base, RefExpr)
             assert isinstance(base.base.node, TypeInfo)
             info = base.base.node
@@ -189,6 +196,10 @@ def add_keys_and_types_from_base(
             if args is None:
                 return
             base_args = args
+        else:
+            assert isinstance(base, CallExpr)
+            assert isinstance(base.analyzed, TypedDictExpr)
+            info = base.analyzed.info
 
         assert info.typeddict_type is not None
         base_typed_dict = info.typeddict_type
diff --git a/test-data/unit/check-typeddict.test b/test-data/unit/check-typeddict.test
index d8022f85574c..625b82936e8c 100644
--- a/test-data/unit/check-typeddict.test
+++ b/test-data/unit/check-typeddict.test
@@ -3438,3 +3438,13 @@ class TotalInTheMiddle(TypedDict, a=1, total=True, b=2, c=3):  # E: Unexpected k
     ...
 [builtins fixtures/dict.pyi]
 [typing fixtures/typing-typeddict.pyi]
+
+[case testCanCreateClassWithFunctionBasedTypedDictBase]
+from mypy_extensions import TypedDict
+
+class Params(TypedDict("Params", {'x': int})):
+    pass
+
+p: Params = {'x': 2}
+reveal_type(p) # N: Revealed type is "TypedDict('__main__.Params', {'x': builtins.int})"
+[builtins fixtures/dict.pyi]