diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 8b4becebead29..15480cb2440ba 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -855,6 +855,7 @@ Groupby/resample/rolling
 - Bug in :meth:`pandas.core.window.Rolling.median` and :meth:`pandas.core.window.Rolling.quantile` where MemoryError is raised with empty window (:issue:`26005`)
 - Bug in :meth:`pandas.core.window.Rolling.median` and :meth:`pandas.core.window.Rolling.quantile` where incorrect results are returned with ``closed='left'`` and ``closed='neither'`` (:issue:`26005`)
 - Improved :class:`pandas.core.window.Rolling`, :class:`pandas.core.window.Window` and :class:`pandas.core.window.EWM` functions to exclude nuisance columns from results instead of raising errors and raise a ``DataError`` only if all columns are nuisance (:issue:`12537`)
+- Bug in :meth:`pandas.core.window.Rolling.max` and :meth:`pandas.core.window.Rolling.min` where incorrect results are returned with an empty variable window`` (:issue:`26005`)
 
 Reshaping
 ^^^^^^^^^
diff --git a/pandas/_libs/window.pyx b/pandas/_libs/window.pyx
index df86f395d6097..6203577e450d9 100644
--- a/pandas/_libs/window.pyx
+++ b/pandas/_libs/window.pyx
@@ -1313,9 +1313,11 @@ cdef _roll_min_max_variable(ndarray[numeric] values,
 
         # if right is open then the first window is empty
         close_offset = 0 if endi[0] > starti[0] else 1
+        # first window's size
+        curr_win_size = endi[0] - starti[0]
 
         for i in range(endi[0], endi[N-1]):
-            if not Q.empty():
+            if not Q.empty() and curr_win_size > 0:
                 output[i-1+close_offset] = calc_mm(
                     minp, nobs, values[Q.front()])
             else:
@@ -1344,7 +1346,7 @@ cdef _roll_min_max_variable(ndarray[numeric] values,
             Q.push_back(i)
             W.push_back(i)
 
-        if not Q.empty():
+        if not Q.empty() and curr_win_size > 0:
             output[N-1] = calc_mm(minp, nobs, values[Q.front()])
         else:
             output[N-1] = NaN
diff --git a/pandas/tests/test_window.py b/pandas/tests/test_window.py
index 889754841a078..8604acb1bd2b2 100644
--- a/pandas/tests/test_window.py
+++ b/pandas/tests/test_window.py
@@ -48,6 +48,12 @@ def win_types_special(request):
     return request.param
 
 
+@pytest.fixture(params=["sum", "mean", "median", "max", "min",
+                        "var", "std", "kurt", "skew"])
+def arithmetic_win_operators(request):
+    return request.param
+
+
 class Base:
 
     _nan_locs = np.arange(20, 40)
@@ -522,6 +528,18 @@ def test_closed(self):
         with pytest.raises(ValueError):
             df.rolling(window=3, closed='neither')
 
+    @pytest.mark.parametrize("closed", ["neither", "left"])
+    def test_closed_empty(self, closed, arithmetic_win_operators):
+        # GH 26005
+        func_name = arithmetic_win_operators
+        ser = pd.Series(data=np.arange(5),
+                        index=pd.date_range("2000", periods=5, freq="2D"))
+        roll = ser.rolling("1D", closed=closed)
+
+        result = getattr(roll, func_name)()
+        expected = pd.Series([np.nan] * 5, index=ser.index)
+        tm.assert_series_equal(result, expected)
+
     @pytest.mark.parametrize("func", ['min', 'max'])
     def test_closed_one_entry(self, func):
         # GH24718