diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index 129f5cedb86c2..e0507991d82ad 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -777,6 +777,7 @@ Numeric
 ^^^^^^^
 - Bug in :func:`read_csv` with ``engine="pyarrow"`` causing rounding errors for large integers (:issue:`52505`)
 - Bug in :meth:`Series.__floordiv__` for :class:`ArrowDtype` with integral dtypes raising for large values (:issue:`56645`)
+- Bug in :meth:`Series.__mod__` and :meth:`Series.__divmod__` for :class:`ArrowDtype` raising ``NotImplementedError`` (:issue:`56693`)
 - Bug in :meth:`Series.pow` not filling missing values correctly (:issue:`55512`)
 
 Conversion
diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index b1164301e6d79..e398c330467de 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -135,6 +135,18 @@ def floordiv_compat(
             result = result.cast(left.type)
         return result
 
+    def divmod_compat(
+        left: pa.ChunkedArray | pa.Array | pa.Scalar,
+        right: pa.ChunkedArray | pa.Array | pa.Scalar,
+    ) -> tuple[pa.ChunkedArray, pa.ChunkedArray]:
+        # (x % y) = x - (x // y) * y
+        # TODO: Should be replaced with corresponding arrow compute
+        # method when available
+        # https://lists.apache.org/thread/h3t6nz1ys2k2hnbrjvwyoxkf70cps8sh
+        floordiv_result = floordiv_compat(left, right)
+        modulus_result = pc.subtract(left, pc.multiply(floordiv_result, right))
+        return floordiv_result, modulus_result
+
     ARROW_ARITHMETIC_FUNCS = {
         "add": pc.add_checked,
         "radd": lambda x, y: pc.add_checked(y, x),
@@ -146,10 +158,10 @@ def floordiv_compat(
         "rtruediv": lambda x, y: pc.divide(y, cast_for_truediv(x, y)),
         "floordiv": lambda x, y: floordiv_compat(x, y),
         "rfloordiv": lambda x, y: floordiv_compat(y, x),
-        "mod": NotImplemented,
-        "rmod": NotImplemented,
-        "divmod": NotImplemented,
-        "rdivmod": NotImplemented,
+        "mod": lambda x, y: divmod_compat(x, y)[1],
+        "rmod": lambda x, y: divmod_compat(y, x)[1],
+        "divmod": lambda x, y: divmod_compat(x, y),
+        "rdivmod": lambda x, y: divmod_compat(y, x),
         "pow": pc.power_checked,
         "rpow": lambda x, y: pc.power_checked(y, x),
     }
@@ -750,6 +762,8 @@ def _evaluate_op_method(self, other, op, arrow_funcs):
             raise NotImplementedError(f"{op.__name__} not implemented.")
 
         result = pc_func(self._pa_array, other)
+        if op is divmod or op is roperator.rdivmod:
+            return type(self)(result[0]), type(self)(result[1])
         return type(self)(result)
 
     def _logical_method(self, other, op):
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index ed1b7b199a16f..15238213f5f52 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -3238,6 +3238,75 @@ def test_arrow_floordiv():
     tm.assert_series_equal(result, expected)
 
 
+modulus_test_cases = [
+    [-7, 3],
+    [-7, -4],
+    [-7, -8],
+    [-7, 8],
+    [7, 8],
+    [7, 3],
+    [7, -3],
+    [-1.2, 1.3],
+    [1.2, 1.3],
+    [-1.2, -1.3],
+    [-1.2, 0.5],
+    [1.2, 0.5],
+    [-1.2, -0.5],
+]
+
+
+@pytest.mark.parametrize("left, right", modulus_test_cases)
+def test_arrow_modulus(left, right):
+    # GH 56693
+    dtype = "int64[pyarrow]" if isinstance(left, int) else "double[pyarrow]"
+    a = pd.Series([left], dtype=dtype)
+    b = pd.Series([right], dtype=dtype)
+    result = a % b
+    # Use stdlib python modulus to baseline.
+    expected = pd.Series([left % right], dtype=dtype)
+    tm.assert_series_equal(result, expected)
+
+
+@pytest.mark.parametrize("left, right", modulus_test_cases)
+def test_arrow_reflected_modulus(left, right):
+    # GH 56693
+    dtype = "int64[pyarrow]" if isinstance(left, int) else "double[pyarrow]"
+    a = pd.Series([left], dtype=dtype)
+    result = right % a
+    # Use stdlib python modulus to baseline.
+    expected = pd.Series([right % left], dtype=dtype)
+    tm.assert_series_equal(result, expected)
+
+
+@pytest.mark.parametrize("left, right", modulus_test_cases)
+def test_arrow_divmod(left, right):
+    # GH 56693
+    dtype = "int64[pyarrow]" if isinstance(left, int) else "double[pyarrow]"
+    a = pd.Series([left], dtype=dtype)
+    b = pd.Series([right], dtype=dtype)
+    result_floordiv, result_modulus = divmod(a, b)
+    # Use stdlib python modulus to baseline.
+    stdlib_baseline = divmod(left, right)
+    expected_floordiv = pd.Series([stdlib_baseline[0]], dtype=dtype)
+    expected_modulus = pd.Series([stdlib_baseline[1]], dtype=dtype)
+    tm.assert_series_equal(result_floordiv, expected_floordiv)
+    tm.assert_series_equal(result_modulus, expected_modulus)
+
+
+@pytest.mark.parametrize("left, right", modulus_test_cases)
+def test_arrow_reflected_divmod(left, right):
+    # GH 56693
+    dtype = "int64[pyarrow]" if isinstance(left, int) else "double[pyarrow]"
+    a = pd.Series([left], dtype=dtype)
+    result_floordiv, result_modulus = divmod(right, a)
+    # Use stdlib python modulus to baseline.
+    stdlib_baseline = divmod(right, left)
+    expected_floordiv = pd.Series([stdlib_baseline[0]], dtype=dtype)
+    expected_modulus = pd.Series([stdlib_baseline[1]], dtype=dtype)
+    tm.assert_series_equal(result_floordiv, expected_floordiv)
+    tm.assert_series_equal(result_modulus, expected_modulus)
+
+
 def test_arrow_floordiv_large_values():
     # GH 55561
     a = pd.Series([1425801600000000000], dtype="int64[pyarrow]")