diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index 903d62fb5c00..22dd2b68c275 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -1431,7 +1431,7 @@ def set_params(self, **kwargs):
     def bin_boundaries(self, vmin, vmax):
         nbins = self._nbins
         if nbins == 'auto':
-            nbins = self.axis.get_tick_space()
+            nbins = min(self.axis.get_tick_space(), 9)
         scale, offset = scale_range(vmin, vmax, nbins)
         if self._integer:
             scale = max(1, scale)