diff --git a/doc/source/whatsnew/v1.3.4.rst b/doc/source/whatsnew/v1.3.4.rst
index 9c9aacc4b0f52..b6ee2d57a0965 100644
--- a/doc/source/whatsnew/v1.3.4.rst
+++ b/doc/source/whatsnew/v1.3.4.rst
@@ -35,6 +35,7 @@ Bug fixes
 ~~~~~~~~~
 - Fixed bug in :meth:`.GroupBy.mean` with datetimelike values including ``NaT`` values returning incorrect results (:issue:`43132`)
 - Fixed bug in :meth:`Series.aggregate` not passing the first ``args`` to the user supplied ``func`` in certain cases (:issue:`43357`)
+- Fixed memory leaks in :meth:`Series.rolling.quantile` and :meth:`Series.rolling.median` (:issue:`43339`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/_libs/window/aggregations.pyx b/pandas/_libs/window/aggregations.pyx
index 1941a3c4a37f0..98201a6f58499 100644
--- a/pandas/_libs/window/aggregations.pyx
+++ b/pandas/_libs/window/aggregations.pyx
@@ -835,6 +835,7 @@ def roll_median_c(const float64_t[:] values, ndarray[int64_t] start,
 
             if not is_monotonic_increasing_bounds:
                 nobs = 0
+                skiplist_destroy(sl)
                 sl = skiplist_init(<int>win)
 
     skiplist_destroy(sl)
@@ -1070,6 +1071,7 @@ def roll_quantile(const float64_t[:] values, ndarray[int64_t] start,
             if i == 0 or not is_monotonic_increasing_bounds:
                 if not is_monotonic_increasing_bounds:
                     nobs = 0
+                    skiplist_destroy(skiplist)
                     skiplist = skiplist_init(<int>win)
 
                 # setup