diff --git a/sklearn/semi_supervised/_label_propagation.py b/sklearn/semi_supervised/_label_propagation.py
index 0ec687aae7d20..eb6657fc4d234 100644
--- a/sklearn/semi_supervised/_label_propagation.py
+++ b/sklearn/semi_supervised/_label_propagation.py
@@ -273,6 +273,7 @@ def fit(self, X, y):
             if self._variant == 'propagation':
                 normalizer = np.sum(
                     self.label_distributions_, axis=1)[:, np.newaxis]
+                normalizer[normalizer == 0] = 1
                 self.label_distributions_ /= normalizer
                 self.label_distributions_ = np.where(unlabeled,
                                                      self.label_distributions_,
@@ -289,6 +290,7 @@ def fit(self, X, y):
             self.n_iter_ += 1
 
         normalizer = np.sum(self.label_distributions_, axis=1)[:, np.newaxis]
+        normalizer[normalizer == 0] = 1
         self.label_distributions_ /= normalizer
 
         # set the transduction item