diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index d1481639ca5a0..58a70a2b66a84 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -831,6 +831,7 @@ Groupby/resample/rolling
 - Bug in :meth:`DataFrame.resample` when resampling on a :class:`ArrowDtype` of ``pyarrow.timestamp`` or ``pyarrow.duration`` type (:issue:`55989`)
 - Bug in :meth:`DataFrame.resample` where bin edges were not correct for :class:`~pandas.tseries.offsets.BusinessDay` (:issue:`55281`)
 - Bug in :meth:`DataFrame.resample` where bin edges were not correct for :class:`~pandas.tseries.offsets.MonthBegin` (:issue:`55271`)
+- Bug in :meth:`DataFrame.rolling` and :meth:`Series.rolling` where either the ``index`` or ``on`` column was :class:`ArrowDtype` with ``pyarrow.timestamp`` type (:issue:`55849`)
 
 Reshaping
 ^^^^^^^^^
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 11a0c7bf18fcb..a0e0a1434e871 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -92,6 +92,7 @@
     pandas_dtype,
 )
 from pandas.core.dtypes.dtypes import (
+    ArrowDtype,
     CategoricalDtype,
     DatetimeTZDtype,
     ExtensionDtype,
@@ -2531,7 +2532,7 @@ def _validate_inferred_freq(
     return freq
 
 
-def dtype_to_unit(dtype: DatetimeTZDtype | np.dtype) -> str:
+def dtype_to_unit(dtype: DatetimeTZDtype | np.dtype | ArrowDtype) -> str:
     """
     Return the unit str corresponding to the dtype's resolution.
 
@@ -2546,4 +2547,8 @@ def dtype_to_unit(dtype: DatetimeTZDtype | np.dtype) -> str:
     """
     if isinstance(dtype, DatetimeTZDtype):
         return dtype.unit
+    elif isinstance(dtype, ArrowDtype):
+        if dtype.kind not in "mM":
+            raise ValueError(f"{dtype=} does not have a resolution.")
+        return dtype.pyarrow_dtype.unit
     return np.datetime_data(dtype)[0]
diff --git a/pandas/core/window/rolling.py b/pandas/core/window/rolling.py
index e78bd258c11ff..68cec16ec9eca 100644
--- a/pandas/core/window/rolling.py
+++ b/pandas/core/window/rolling.py
@@ -14,7 +14,6 @@
     Any,
     Callable,
     Literal,
-    cast,
 )
 
 import numpy as np
@@ -39,6 +38,7 @@
     is_numeric_dtype,
     needs_i8_conversion,
 )
+from pandas.core.dtypes.dtypes import ArrowDtype
 from pandas.core.dtypes.generic import (
     ABCDataFrame,
     ABCSeries,
@@ -104,6 +104,7 @@
         NDFrameT,
         QuantileInterpolation,
         WindowingRankType,
+        npt,
     )
 
     from pandas import (
@@ -404,11 +405,12 @@ def _insert_on_column(self, result: DataFrame, obj: DataFrame) -> None:
                 result[name] = extra_col
 
     @property
-    def _index_array(self):
+    def _index_array(self) -> npt.NDArray[np.int64] | None:
         # TODO: why do we get here with e.g. MultiIndex?
-        if needs_i8_conversion(self._on.dtype):
-            idx = cast("PeriodIndex | DatetimeIndex | TimedeltaIndex", self._on)
-            return idx.asi8
+        if isinstance(self._on, (PeriodIndex, DatetimeIndex, TimedeltaIndex)):
+            return self._on.asi8
+        elif isinstance(self._on.dtype, ArrowDtype) and self._on.dtype.kind in "mM":
+            return self._on.to_numpy(dtype=np.int64)
         return None
 
     def _resolve_output(self, out: DataFrame, obj: DataFrame) -> DataFrame:
@@ -439,7 +441,7 @@ def _apply_series(
         self, homogeneous_func: Callable[..., ArrayLike], name: str | None = None
     ) -> Series:
         """
-        Series version of _apply_blockwise
+        Series version of _apply_columnwise
         """
         obj = self._create_data(self._selected_obj)
 
@@ -455,7 +457,7 @@ def _apply_series(
         index = self._slice_axis_for_step(obj.index, result)
         return obj._constructor(result, index=index, name=obj.name)
 
-    def _apply_blockwise(
+    def _apply_columnwise(
         self,
         homogeneous_func: Callable[..., ArrayLike],
         name: str,
@@ -614,7 +616,7 @@ def calc(x):
             return result
 
         if self.method == "single":
-            return self._apply_blockwise(homogeneous_func, name, numeric_only)
+            return self._apply_columnwise(homogeneous_func, name, numeric_only)
         else:
             return self._apply_tablewise(homogeneous_func, name, numeric_only)
 
@@ -1232,7 +1234,9 @@ def calc(x):
 
             return result
 
-        return self._apply_blockwise(homogeneous_func, name, numeric_only)[:: self.step]
+        return self._apply_columnwise(homogeneous_func, name, numeric_only)[
+            :: self.step
+        ]
 
     @doc(
         _shared_docs["aggregate"],
@@ -1868,6 +1872,7 @@ def _validate(self):
         if (
             self.obj.empty
             or isinstance(self._on, (DatetimeIndex, TimedeltaIndex, PeriodIndex))
+            or (isinstance(self._on.dtype, ArrowDtype) and self._on.dtype.kind in "mM")
         ) and isinstance(self.window, (str, BaseOffset, timedelta)):
             self._validate_datetimelike_monotonic()
 
diff --git a/pandas/tests/window/test_timeseries_window.py b/pandas/tests/window/test_timeseries_window.py
index c99fc8a8eb60f..bd0fadeb3e475 100644
--- a/pandas/tests/window/test_timeseries_window.py
+++ b/pandas/tests/window/test_timeseries_window.py
@@ -1,9 +1,12 @@
 import numpy as np
 import pytest
 
+import pandas.util._test_decorators as td
+
 from pandas import (
     DataFrame,
     DatetimeIndex,
+    Index,
     MultiIndex,
     NaT,
     Series,
@@ -697,3 +700,16 @@ def test_nat_axis_error(msg, axis):
     with pytest.raises(ValueError, match=f"{msg} values must not have NaT"):
         with tm.assert_produces_warning(FutureWarning, match=warn_msg):
             df.rolling("D", axis=axis).mean()
+
+
+@td.skip_if_no("pyarrow")
+def test_arrow_datetime_axis():
+    # GH 55849
+    expected = Series(
+        np.arange(5, dtype=np.float64),
+        index=Index(
+            date_range("2020-01-01", periods=5), dtype="timestamp[ns][pyarrow]"
+        ),
+    )
+    result = expected.rolling("1D").sum()
+    tm.assert_series_equal(result, expected)