diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 950082f9281c5..7f2c90bc89a9a 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -142,7 +142,7 @@ Timezones
 
 Numeric
 ^^^^^^^
--
+- Bug in ``np.matmul`` with :class:`Index` inputs raising a ``TypeError`` (:issue:`57079`)
 -
 
 Conversion
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index bf20525e2c7fd..4b200c447cb4d 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -951,6 +951,9 @@ def __array_ufunc__(self, ufunc: np.ufunc, method: str_t, *inputs, **kwargs):
         elif method == "reduce":
             result = lib.item_from_zerodim(result)
             return result
+        elif is_scalar(result):
+            # e.g. matmul
+            return result
 
         if result.dtype == np.float16:
             result = result.astype(np.float32)
diff --git a/pandas/tests/series/test_ufunc.py b/pandas/tests/series/test_ufunc.py
index 9d13ebf740eab..3ef319174313d 100644
--- a/pandas/tests/series/test_ufunc.py
+++ b/pandas/tests/series/test_ufunc.py
@@ -427,6 +427,13 @@ def test_np_matmul():
     tm.assert_frame_equal(expected, result)
 
 
+@pytest.mark.parametrize("box", [pd.Index, pd.Series])
+def test_np_matmul_1D(box):
+    result = np.matmul(box([1, 2]), box([2, 3]))
+    assert result == 8
+    assert isinstance(result, np.int64)
+
+
 def test_array_ufuncs_for_many_arguments():
     # GH39853
     def add3(x, y, z):