diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
index 9db44b7994bb..c77d2a4a7868 100644
--- a/lib/mpl_toolkits/mplot3d/axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -387,6 +387,10 @@ def apply_aspect(self, position=None):
 
     @martist.allow_rasterization
     def draw(self, renderer):
+        if renderer is None:
+            raise RuntimeError("No renderer defined")
+        if not self.get_visible():
+            return
         self._unstale_viewLim()
 
         # draw the background patch
diff --git a/lib/mpl_toolkits/tests/test_mplot3d_visibility.py b/lib/mpl_toolkits/tests/test_mplot3d_visibility.py
new file mode 100644
index 000000000000..25b5dd305aba
--- /dev/null
+++ b/lib/mpl_toolkits/tests/test_mplot3d_visibility.py
@@ -0,0 +1,33 @@
+import numpy as np
+
+from matplotlib.figure import Figure
+from matplotlib.backends.backend_agg import FigureCanvasAgg
+
+
+def test_axes3d_respects_set_visible_false():
+    fig = Figure(figsize=(4, 2), dpi=100)
+    canvas = FigureCanvasAgg(fig)
+
+    ax1 = fig.add_subplot(1, 2, 1, projection='3d')
+    ax2 = fig.add_subplot(1, 2, 2, projection='3d')
+
+    ax1.scatter([1], [1], [1])
+    ax2.scatter([1], [1], [1], c='r')
+
+    # Hide left axes entirely.
+    ax1.set_visible(False)
+
+    # Draw and examine pixels.
+    canvas.draw()
+    im = np.asarray(canvas.buffer_rgba())
+
+    # Use a margin to avoid antialiasing artifacts at figure edges.
+    h, w, _ = im.shape
+    margin = 5
+    left_half = im[margin:-margin, margin:w // 2 - margin, :3]
+
+    # Background is typically uniform; sample a corner pixel.
+    bg = im[margin, margin, :3]
+
+    # Assert that the left half contains only background pixels.
+    assert np.all(left_half == bg)