diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index 32044d1fc233a..89e916153ffa8 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -2086,6 +2086,23 @@ def interpolate(
         See NDFrame.interpolate.__doc__.
         """
         # NB: we return type(self) even if copy=False
+        if not self.dtype._is_numeric:
+            raise ValueError("Values must be numeric.")
+
+        if (
+            not pa_version_under13p0
+            and method == "linear"
+            and limit_area is None
+            and limit is None
+            and limit_direction == "forward"
+        ):
+            values = self._pa_array.combine_chunks()
+            na_value = pa.array([None], type=values.type)
+            y_diff_2 = pc.fill_null_backward(pc.pairwise_diff_checked(values, period=2))
+            prev_values = pa.concat_arrays([na_value, values[:-2], na_value])
+            interps = pc.add_checked(prev_values, pc.divide_checked(y_diff_2, 2))
+            return type(self)(pc.coalesce(self._pa_array, interps))
+
         mask = self.isna()
         if self.dtype.kind == "f":
             data = self._pa_array.to_numpy()
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index b49f107859159..9f8985788cb95 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -3436,6 +3436,26 @@ def test_string_to_datetime_parsing_cast():
     tm.assert_series_equal(result, expected)
 
 
+@pytest.mark.skipif(
+    pa_version_under13p0, reason="pairwise_diff_checked not implemented in pyarrow"
+)
+def test_interpolate_not_numeric(data):
+    if not data.dtype._is_numeric:
+        with pytest.raises(ValueError, match="Values must be numeric."):
+            pd.Series(data).interpolate()
+
+
+@pytest.mark.skipif(
+    pa_version_under13p0, reason="pairwise_diff_checked not implemented in pyarrow"
+)
+@pytest.mark.parametrize("dtype", ["int64[pyarrow]", "float64[pyarrow]"])
+def test_interpolate_linear(dtype):
+    ser = pd.Series([None, 1, 2, None, 4, None], dtype=dtype)
+    result = ser.interpolate()
+    expected = pd.Series([None, 1, 2, 3, 4, None], dtype=dtype)
+    tm.assert_series_equal(result, expected)
+
+
 def test_string_to_time_parsing_cast():
     # GH 56463
     string_times = ["11:41:43.076160"]