diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 0f78f07af4a89..13e1ddd153ccb 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -711,6 +711,7 @@ Period
 Plotting
 ^^^^^^^^
 - Bug in :meth:`.DataFrameGroupBy.boxplot` failed when there were multiple groupings (:issue:`14701`)
+- Bug in :meth:`DataFrame.plot.bar` with ``stacked=True`` where labels on stacked bars with zero-height segments were incorrectly positioned at the base instead of the label position of the previous segment (:issue:`59429`)
 - Bug in :meth:`DataFrame.plot.line` raising ``ValueError`` when set both color and a ``dict`` style (:issue:`59461`)
 - Bug in :meth:`DataFrame.plot` that causes a shift to the right when the frequency multiplier is greater than one. (:issue:`57587`)
 - Bug in :meth:`Series.plot` with ``kind="pie"`` with :class:`ArrowDtype` (:issue:`59192`)
diff --git a/pandas/plotting/_matplotlib/core.py b/pandas/plotting/_matplotlib/core.py
index 505db4b807cfc..1035150302d2c 100644
--- a/pandas/plotting/_matplotlib/core.py
+++ b/pandas/plotting/_matplotlib/core.py
@@ -1960,7 +1960,7 @@ def _make_plot(self, fig: Figure) -> None:
                 )
                 ax.set_title(label)
             elif self.stacked:
-                mask = y > 0
+                mask = y >= 0
                 start = np.where(mask, pos_prior, neg_prior) + self._start_base
                 w = self.bar_width / 2
                 rect = self._plot(
diff --git a/pandas/tests/plotting/frame/test_frame.py b/pandas/tests/plotting/frame/test_frame.py
index b39f953da1ee6..087280ed3e01d 100644
--- a/pandas/tests/plotting/frame/test_frame.py
+++ b/pandas/tests/plotting/frame/test_frame.py
@@ -774,6 +774,16 @@ def test_bar_nan_stacked(self):
         expected = [0.0, 0.0, 0.0, 10.0, 0.0, 20.0, 15.0, 10.0, 40.0]
         assert result == expected
 
+    def test_bar_stacked_label_position_with_zero_height(self):
+        # GH 59429
+        df = DataFrame({"A": [3, 0, 1], "B": [0, 2, 4], "C": [5, 0, 2]})
+        ax = df.plot.bar(stacked=True)
+        ax.bar_label(ax.containers[-1])
+        expected = [8.0, 2.0, 7.0]
+        result = [text.xy[1] for text in ax.texts]
+        tm.assert_almost_equal(result, expected)
+        plt.close("all")
+
     @pytest.mark.parametrize("idx", [Index, pd.CategoricalIndex])
     def test_bar_categorical(self, idx):
         # GH 13019