diff --git a/asv_bench/benchmarks/rolling.py b/asv_bench/benchmarks/rolling.py
index 659b6591fbd4b..7aefad6e2929b 100644
--- a/asv_bench/benchmarks/rolling.py
+++ b/asv_bench/benchmarks/rolling.py
@@ -113,4 +113,20 @@ def time_quantile(self, constructor, window, dtype, percentile,
         self.roll.quantile(percentile, interpolation=interpolation)
 
 
+class PeakMemFixed(object):
+
+    def setup(self):
+        N = 10
+        arr = 100 * np.random.random(N)
+        self.roll = pd.Series(arr).rolling(10)
+
+    def peakmem_fixed(self):
+        # GH 25926
+        # This is to detect memory leaks in rolling operations.
+        # To save time this is only ran on one method.
+        # 6000 iterations is enough for most types of leaks to be detected
+        for x in range(6000):
+            self.roll.max()
+
+
 from .pandas_vb_common import setup  # noqa: F401
diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 94f8fd16ea85a..6502063c71125 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -372,6 +372,7 @@ Groupby/Resample/Rolling
 - Bug in :func:`pandas.core.groupby.GroupBy.agg` when applying a aggregation function to timezone aware data (:issue:`23683`)
 - Bug in :func:`pandas.core.groupby.GroupBy.first` and :func:`pandas.core.groupby.GroupBy.last` where timezone information would be dropped (:issue:`21603`)
 - Ensured that ordering of outputs in ``groupby`` aggregation functions is consistent across all versions of Python (:issue:`25692`)
+- Bug in :meth:`pandas.core.window.Rolling.min` and :meth:`pandas.core.window.Rolling.max` that caused a memory leak (:issue:`25893`)
 - Bug in :func:`idxmax` and :func:`idxmin` on :meth:`DataFrame.groupby` with datetime column would return incorrect dtype (:issue:`25444`, :issue:`15306`)
 
 
diff --git a/pandas/_libs/window.pyx b/pandas/_libs/window.pyx
index cc5b3b63f5b04..29a21c06c064e 100644
--- a/pandas/_libs/window.pyx
+++ b/pandas/_libs/window.pyx
@@ -1263,7 +1263,7 @@ cdef _roll_min_max(ndarray[numeric] values, int64_t win, int64_t minp,
         return _roll_min_max_variable(values, starti, endi, N, win, minp,
                                       is_max)
     else:
-        return _roll_min_max_fixed(values, starti, endi, N, win, minp, is_max)
+        return _roll_min_max_fixed(values, N, win, minp, is_max)
 
 
 cdef _roll_min_max_variable(ndarray[numeric] values,
@@ -1349,8 +1349,6 @@ cdef _roll_min_max_variable(ndarray[numeric] values,
 
 
 cdef _roll_min_max_fixed(ndarray[numeric] values,
-                         ndarray[int64_t] starti,
-                         ndarray[int64_t] endi,
                          int64_t N,
                          int64_t win,
                          int64_t minp,