diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index 67b4052b386c0..c878fd2664dc4 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -576,6 +576,7 @@ Strings
 ^^^^^^^
 - Bug in :func:`pandas.api.types.is_string_dtype` while checking object array with no elements is of the string dtype (:issue:`54661`)
 - Bug in :meth:`DataFrame.apply` failing when ``engine="numba"`` and columns or index have ``StringDtype`` (:issue:`56189`)
+- Bug in :meth:`Series.__mul__` for :class:`ArrowDtype` with ``pyarrow.string`` dtype and ``string[pyarrow]`` for the pyarrow backend (:issue:`51970`)
 - Bug in :meth:`Series.str.startswith` and :meth:`Series.str.endswith` with arguments of type ``tuple[str, ...]`` for ``string[pyarrow]`` (:issue:`54942`)
 
 Interval
diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index 1609bf50a834a..e7a50dbba9935 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -668,16 +668,22 @@ def _evaluate_op_method(self, other, op, arrow_funcs):
         pa_type = self._pa_array.type
         other = self._box_pa(other)
 
-        if (pa.types.is_string(pa_type) or pa.types.is_binary(pa_type)) and op in [
-            operator.add,
-            roperator.radd,
-        ]:
-            sep = pa.scalar("", type=pa_type)
-            if op is operator.add:
-                result = pc.binary_join_element_wise(self._pa_array, other, sep)
-            else:
-                result = pc.binary_join_element_wise(other, self._pa_array, sep)
-            return type(self)(result)
+        if pa.types.is_string(pa_type) or pa.types.is_binary(pa_type):
+            if op in [operator.add, roperator.radd, operator.mul, roperator.rmul]:
+                sep = pa.scalar("", type=pa_type)
+                if op is operator.add:
+                    result = pc.binary_join_element_wise(self._pa_array, other, sep)
+                elif op is roperator.radd:
+                    result = pc.binary_join_element_wise(other, self._pa_array, sep)
+                else:
+                    if not (
+                        isinstance(other, pa.Scalar) and pa.types.is_integer(other.type)
+                    ):
+                        raise TypeError("Can only string multiply by an integer.")
+                    result = pc.binary_join_element_wise(
+                        *([self._pa_array] * other.as_py()), sep
+                    )
+                return type(self)(result)
 
         if (
             isinstance(other, pa.Scalar)
diff --git a/pandas/tests/arrays/string_/test_string.py b/pandas/tests/arrays/string_/test_string.py
index 524a6632e5544..3e11062b8384e 100644
--- a/pandas/tests/arrays/string_/test_string.py
+++ b/pandas/tests/arrays/string_/test_string.py
@@ -176,12 +176,7 @@ def test_add_sequence(dtype):
     tm.assert_extension_array_equal(result, expected)
 
 
-def test_mul(dtype, request, arrow_string_storage):
-    if dtype.storage in arrow_string_storage:
-        reason = "unsupported operand type(s) for *: 'ArrowStringArray' and 'int'"
-        mark = pytest.mark.xfail(raises=NotImplementedError, reason=reason)
-        request.applymarker(mark)
-
+def test_mul(dtype):
     a = pd.array(["a", "b", None], dtype=dtype)
     result = a * 2
     expected = pd.array(["aa", "bb", None], dtype=dtype)
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index 9e70a59932701..3ce3cee9714e4 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -965,8 +965,16 @@ def _get_arith_xfail_marker(self, opname, pa_dtype):
     def test_arith_series_with_scalar(self, data, all_arithmetic_operators, request):
         pa_dtype = data.dtype.pyarrow_dtype
 
-        if all_arithmetic_operators == "__rmod__" and (pa.types.is_binary(pa_dtype)):
+        if all_arithmetic_operators == "__rmod__" and pa.types.is_binary(pa_dtype):
             pytest.skip("Skip testing Python string formatting")
+        elif all_arithmetic_operators in ("__rmul__", "__mul__") and (
+            pa.types.is_binary(pa_dtype) or pa.types.is_string(pa_dtype)
+        ):
+            request.applymarker(
+                pytest.mark.xfail(
+                    raises=TypeError, reason="Can only string multiply by an integer."
+                )
+            )
 
         mark = self._get_arith_xfail_marker(all_arithmetic_operators, pa_dtype)
         if mark is not None:
@@ -981,6 +989,14 @@ def test_arith_frame_with_scalar(self, data, all_arithmetic_operators, request):
             pa.types.is_string(pa_dtype) or pa.types.is_binary(pa_dtype)
         ):
             pytest.skip("Skip testing Python string formatting")
+        elif all_arithmetic_operators in ("__rmul__", "__mul__") and (
+            pa.types.is_binary(pa_dtype) or pa.types.is_string(pa_dtype)
+        ):
+            request.applymarker(
+                pytest.mark.xfail(
+                    raises=TypeError, reason="Can only string multiply by an integer."
+                )
+            )
 
         mark = self._get_arith_xfail_marker(all_arithmetic_operators, pa_dtype)
         if mark is not None:
@@ -1004,6 +1020,14 @@ def test_arith_series_with_array(self, data, all_arithmetic_operators, request):
                     ),
                 )
             )
+        elif all_arithmetic_operators in ("__rmul__", "__mul__") and (
+            pa.types.is_binary(pa_dtype) or pa.types.is_string(pa_dtype)
+        ):
+            request.applymarker(
+                pytest.mark.xfail(
+                    raises=TypeError, reason="Can only string multiply by an integer."
+                )
+            )
 
         mark = self._get_arith_xfail_marker(all_arithmetic_operators, pa_dtype)
         if mark is not None: