diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index 45b5c16415f9d..a60d4806252dd 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -187,6 +187,7 @@ Plotting
 Groupby/resample/rolling
 ^^^^^^^^^^^^^^^^^^^^^^^^
 - Bug in :meth:`DataFrameGroupBy.idxmin`, :meth:`SeriesGroupBy.idxmin`, :meth:`DataFrameGroupBy.idxmax`, :meth:`SeriesGroupBy.idxmax` return wrong dtype when used on empty DataFrameGroupBy or SeriesGroupBy (:issue:`51423`)
+- Bug in weighted rolling aggregations when specifying ``min_periods=0`` (:issue:`51449`)
 -
 
 Reshaping
diff --git a/pandas/core/window/rolling.py b/pandas/core/window/rolling.py
index 97b3f23d65b44..46ce5950a1465 100644
--- a/pandas/core/window/rolling.py
+++ b/pandas/core/window/rolling.py
@@ -1204,7 +1204,11 @@ def homogeneous_func(values: np.ndarray):
             def calc(x):
                 additional_nans = np.array([np.nan] * offset)
                 x = np.concatenate((x, additional_nans))
-                return func(x, window, self.min_periods or len(window))
+                return func(
+                    x,
+                    window,
+                    self.min_periods if self.min_periods is not None else len(window),
+                )
 
             with np.errstate(all="ignore"):
                 # Our weighted aggregations return memoryviews
diff --git a/pandas/tests/window/test_win_type.py b/pandas/tests/window/test_win_type.py
index 8438e0727c174..a0d052257ec6b 100644
--- a/pandas/tests/window/test_win_type.py
+++ b/pandas/tests/window/test_win_type.py
@@ -321,16 +321,16 @@ def test_cmov_window_frame(f, xp, step):
     tm.assert_frame_equal(xp, rs)
 
 
+@pytest.mark.parametrize("min_periods", [0, 1, 2, 3, 4, 5])
 @td.skip_if_no_scipy
-def test_cmov_window_na_min_periods(step):
-    # min_periods
+def test_cmov_window_na_min_periods(step, min_periods):
     vals = Series(np.random.randn(10))
     vals[4] = np.nan
     vals[8] = np.nan
 
-    xp = vals.rolling(5, min_periods=4, center=True, step=step).mean()
+    xp = vals.rolling(5, min_periods=min_periods, center=True, step=step).mean()
     rs = vals.rolling(
-        5, win_type="boxcar", min_periods=4, center=True, step=step
+        5, win_type="boxcar", min_periods=min_periods, center=True, step=step
     ).mean()
     tm.assert_series_equal(xp, rs)