diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
index 1ecc6186a258..d6aeb7d366f8 100644
--- a/lib/matplotlib/axes/_axes.py
+++ b/lib/matplotlib/axes/_axes.py
@@ -1083,10 +1083,10 @@ def hlines(self, y, xmin, xmax, colors=None, linestyles='solid',
         lines._internal_update(kwargs)
 
         if len(y) > 0:
-            minx = min(xmin.min(), xmax.min())
-            maxx = max(xmin.max(), xmax.max())
-            miny = y.min()
-            maxy = y.max()
+            minx = min(np.nanmin(xmin), np.nanmin(xmax))
+            maxx = max(np.nanmax(xmin), np.nanmax(xmax))
+            miny = np.nanmin(y)
+            maxy = np.nanmax(y)
 
             corners = (minx, miny), (maxx, maxy)
 
@@ -1162,10 +1162,10 @@ def vlines(self, x, ymin, ymax, colors=None, linestyles='solid',
         lines._internal_update(kwargs)
 
         if len(x) > 0:
-            minx = x.min()
-            maxx = x.max()
-            miny = min(ymin.min(), ymax.min())
-            maxy = max(ymin.max(), ymax.max())
+            minx = np.nanmin(x)
+            maxx = np.nanmax(x)
+            miny = min(np.nanmin(ymin), np.nanmin(ymax))
+            maxy = max(np.nanmax(ymin), np.nanmax(ymax))
 
             corners = (minx, miny), (maxx, maxy)
             self.update_datalim(corners)
@@ -2674,7 +2674,7 @@ def sign(x):
                 extrema = max(x0, x1) if dat >= 0 else min(x0, x1)
                 length = abs(x0 - x1)
 
-            if err is None:
+            if err is None or np.size(err) == 0:
                 endpt = extrema
             elif orientation == "vertical":
                 endpt = err[:, 1].max() if dat >= 0 else err[:, 1].min()
@@ -3504,7 +3504,9 @@ def apply_mask(arrays, mask): return [array[mask] for array in arrays]
                     f"'{dep_axis}err' (shape: {np.shape(err)}) must be a "
                     f"scalar or a 1D or (2, n) array-like whose shape matches "
                     f"'{dep_axis}' (shape: {np.shape(dep)})") from None
-            if np.any(err < -err):  # like err<0, but also works for timedelta.
+            res = np.zeros_like(err, dtype=bool)  # Default in case of nan
+            if np.any(np.less(err, -err, out=res, where=(err == err))):
+                # like err<0, but also works for timedelta and nan.
                 raise ValueError(
                     f"'{dep_axis}err' must not contain negative values")
             # This is like
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 66bf83c542f1..6be9330d28da 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -7549,6 +7549,26 @@ def test_bar_label_nan_ydata_inverted():
     assert labels[0].get_va() == 'bottom'
 
 
+def test_nan_barlabels():
+    fig, ax = plt.subplots()
+    bars = ax.bar([1, 2, 3], [np.nan, 1, 2], yerr=[0.2, 0.4, 0.6])
+    labels = ax.bar_label(bars)
+    assert [l.get_text() for l in labels] == ['', '1', '2']
+    assert np.allclose(ax.get_ylim(), (0.0, 3.0))
+
+    fig, ax = plt.subplots()
+    bars = ax.bar([1, 2, 3], [0, 1, 2], yerr=[0.2, np.nan, 0.6])
+    labels = ax.bar_label(bars)
+    assert [l.get_text() for l in labels] == ['0', '1', '2']
+    assert np.allclose(ax.get_ylim(), (-0.5, 3.0))
+
+    fig, ax = plt.subplots()
+    bars = ax.bar([1, 2, 3], [np.nan, 1, 2], yerr=[np.nan, np.nan, 0.6])
+    labels = ax.bar_label(bars)
+    assert [l.get_text() for l in labels] == ['', '1', '2']
+    assert np.allclose(ax.get_ylim(), (0.0, 3.0))
+
+
 def test_patch_bounds():  # PR 19078
     fig, ax = plt.subplots()
     ax.add_patch(mpatches.Wedge((0, -1), 1.05, 60, 120, 0.1))