diff --git a/sklearn/cluster/hierarchical.py b/sklearn/cluster/hierarchical.py
index 9c3e43e901bf5..3ba6c4978063d 100644
--- a/sklearn/cluster/hierarchical.py
+++ b/sklearn/cluster/hierarchical.py
@@ -379,6 +379,10 @@ def linkage_tree(X, connectivity=None, n_components=None,
             'Unknown linkage option, linkage should be one '
             'of %s, but %s was given' % (linkage_choices.keys(), linkage))
 
+    if affinity == 'cosine' and np.any(~np.any(X, axis=1)):
+        raise ValueError(
+            'Cosine affinity cannot be used when X contains zero vectors')
+
     if connectivity is None:
         from scipy.cluster import hierarchy     # imports PIL
 
diff --git a/sklearn/cluster/tests/test_hierarchical.py b/sklearn/cluster/tests/test_hierarchical.py
index cbafac1bc355e..65c66f480bb88 100644
--- a/sklearn/cluster/tests/test_hierarchical.py
+++ b/sklearn/cluster/tests/test_hierarchical.py
@@ -115,6 +115,15 @@ def test_height_linkage_tree():
         assert_true(len(children) + n_leaves == n_nodes)
 
 
+def test_zero_cosine_linkage_tree():
+    # Check that zero vectors in X produce an error when
+    # 'cosine' affinity is used
+    X = np.array([[0, 1],
+                  [0, 0]])
+    msg = 'Cosine affinity cannot be used when X contains zero vectors'
+    assert_raise_message(ValueError, msg, linkage_tree, X, affinity='cosine')
+
+
 def test_agglomerative_clustering():
     # Check that we obtain the correct number of clusters with
     # agglomerative clustering.