diff --git a/lib/mpl_toolkits/mplot3d/art3d.py b/lib/mpl_toolkits/mplot3d/art3d.py
index b0d7312bff3d..c165a3e1e453 100644
--- a/lib/mpl_toolkits/mplot3d/art3d.py
+++ b/lib/mpl_toolkits/mplot3d/art3d.py
@@ -360,7 +360,7 @@ def draw(self, renderer):
         if np.any(scale_mask):
             mask = np.broadcast_to(
                 scale_mask,
-                (len(self._verts3d), *self._verts3d[0].shape)
+                (len(self._verts3d), *np.shape(self._verts3d[0]))
             )
             xs3d, ys3d, zs3d = np.ma.array(self._verts3d,
                                            dtype=float, mask=mask).filled(np.nan)
diff --git a/lib/mpl_toolkits/mplot3d/tests/test_art3d.py b/lib/mpl_toolkits/mplot3d/tests/test_art3d.py
index aca943f9e0c0..c38f0c744531 100644
--- a/lib/mpl_toolkits/mplot3d/tests/test_art3d.py
+++ b/lib/mpl_toolkits/mplot3d/tests/test_art3d.py
@@ -13,6 +13,18 @@
 )
 
 
+def test_line3d_set_data_3d_list_with_nan():
+    # Regression test for #32127: set_data_3d stores array-like as given, and
+    # draw must not require ndarray .shape when a coordinate is non-finite.
+    fig = plt.figure()
+    ax = fig.add_subplot(projection="3d")
+    line, = ax.plot([0.0], [0.0], [0.0])
+    xs, ys, zs = [float("nan")], [float("nan")], [float("nan")]
+    line.set_data_3d(xs, ys, zs)
+    assert line.get_data_3d() == (xs, ys, zs)
+    fig.canvas.draw()
+
+
 @pytest.mark.parametrize("zdir, expected", [
     ("x", (1, 0, 0)),
     ("y", (0, 1, 0)),