diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index e6bc422b52e89..8767a0c2d5ea1 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -742,6 +742,7 @@ Groupby/Resample/Rolling
 - Bug in :meth:`pandas.core.groupby.SeriesGroupBy.transform` where transforming an empty group would raise a ``ValueError`` (:issue:`26208`)
 - Bug in :meth:`pandas.core.frame.DataFrame.groupby` where passing a :class:`pandas.core.groupby.grouper.Grouper` would return incorrect groups when using the ``.groups`` accessor (:issue:`26326`)
 - Bug in :meth:`pandas.core.groupby.GroupBy.agg` where incorrect results are returned for uint64 columns. (:issue:`26310`)
+- Bug in :meth:`pandas.core.window.Rolling.median` and :meth:`pandas.core.window.Rolling.quantile` where MemoryError is raised with empty window (:issue:`26005`)
 
 Reshaping
 ^^^^^^^^^
diff --git a/pandas/_libs/window.pyx b/pandas/_libs/window.pyx
index 48b554ca02a9d..3305fea06f003 100644
--- a/pandas/_libs/window.pyx
+++ b/pandas/_libs/window.pyx
@@ -1099,6 +1099,10 @@ def roll_median_c(ndarray[float64_t] values, int64_t win, int64_t minp,
         use_mock=False)
     output = np.empty(N, dtype=float)
 
+    if win == 0:
+        output[:] = NaN
+        return output
+
     sl = skiplist_init(<int>win)
     if sl == NULL:
         raise MemoryError("skiplist_init failed")
@@ -1486,6 +1490,11 @@ def roll_quantile(ndarray[float64_t, cast=True] values, int64_t win,
         minp, index, closed,
         use_mock=False)
     output = np.empty(N, dtype=float)
+
+    if win == 0:
+        output[:] = NaN
+        return output
+
     skiplist = skiplist_init(<int>win)
     if skiplist == NULL:
         raise MemoryError("skiplist_init failed")
diff --git a/pandas/tests/test_window.py b/pandas/tests/test_window.py
index bc6946cbade4c..31baf4475214f 100644
--- a/pandas/tests/test_window.py
+++ b/pandas/tests/test_window.py
@@ -608,6 +608,17 @@ def tests_empty_df_rolling(self, roller):
         result = DataFrame(index=pd.DatetimeIndex([])).rolling(roller).sum()
         tm.assert_frame_equal(result, expected)
 
+    def test_empty_window_median_quantile(self):
+        # GH 26005
+        expected = pd.Series([np.nan, np.nan, np.nan])
+        roll = pd.Series(np.arange(3)).rolling(0)
+
+        result = roll.median()
+        tm.assert_series_equal(result, expected)
+
+        result = roll.quantile(0.1)
+        tm.assert_series_equal(result, expected)
+
     def test_missing_minp_zero(self):
         # https://github.com/pandas-dev/pandas/pull/18921
         # minp=0