diff --git a/sklearn/feature_selection/base.py b/sklearn/feature_selection/base.py
index 7a5208dd49c16..16f2d274ace62 100644
--- a/sklearn/feature_selection/base.py
+++ b/sklearn/feature_selection/base.py
@@ -5,6 +5,7 @@
 # License: BSD 3 clause
 
 from abc import ABCMeta, abstractmethod
+from warnings import warn
 
 import numpy as np
 from scipy.sparse import issparse, csc_matrix
@@ -73,6 +74,11 @@ def transform(self, X):
         """
         X = check_array(X, accept_sparse='csr')
         mask = self.get_support()
+        if not mask.any():
+            warn("No features were selected: either the data is"
+                 " too noisy or the selection test too strict.",
+                 UserWarning)
+            return np.empty(0).reshape((X.shape[0], 0))
         if len(mask) != X.shape[1]:
             raise ValueError("X has a different shape than during fitting.")
         return check_array(X, accept_sparse='csr')[:, safe_mask(X, mask)]
diff --git a/sklearn/feature_selection/tests/test_feature_select.py b/sklearn/feature_selection/tests/test_feature_select.py
index 769df7783a6ad..4d46d257c1189 100644
--- a/sklearn/feature_selection/tests/test_feature_select.py
+++ b/sklearn/feature_selection/tests/test_feature_select.py
@@ -16,6 +16,7 @@
 from sklearn.utils.testing import assert_less
 from sklearn.utils.testing import assert_warns
 from sklearn.utils.testing import ignore_warnings
+from sklearn.utils.testing import assert_warns_message
 from sklearn.utils import safe_mask
 
 from sklearn.datasets.samples_generator import (make_classification,
@@ -251,10 +252,13 @@ def test_select_kbest_zero():
                                shuffle=False, random_state=0)
 
     univariate_filter = SelectKBest(f_classif, k=0)
-    univariate_filter.fit(X, y).transform(X)
+    univariate_filter.fit(X, y)
     support = univariate_filter.get_support()
     gtruth = np.zeros(10, dtype=bool)
     assert_array_equal(support, gtruth)
+    X_selected = assert_warns_message(UserWarning, 'No features were selected',
+                                      univariate_filter.transform, X)
+    assert_equal(X_selected.shape, (20, 0))
 
 
 def test_select_fpr_classif():
@@ -585,3 +589,24 @@ def test_f_classif_constant_feature():
     X, y = make_classification(n_samples=10, n_features=5)
     X[:, 0] = 2.0
     assert_warns(UserWarning, f_classif, X, y)
+
+
+def test_no_feature_selected():
+    rng = np.random.RandomState(0)
+
+    # Generate random uncorrelated data: a strict univariate test should
+    # rejects all the features
+    X = rng.rand(40, 10)
+    y = rng.randint(0, 4, size=40)
+    strict_selectors = [
+        SelectFwe(alpha=0.01).fit(X, y),
+        SelectFdr(alpha=0.01).fit(X, y),
+        SelectFpr(alpha=0.01).fit(X, y),
+        SelectPercentile(percentile=0).fit(X, y),
+        SelectKBest(k=0).fit(X, y),
+    ]
+    for selector in strict_selectors:
+        assert_array_equal(selector.get_support(), np.zeros(10))
+        X_selected = assert_warns_message(
+            UserWarning, 'No features were selected', selector.transform, X)
+        assert_equal(X_selected.shape, (40, 0))
diff --git a/sklearn/feature_selection/univariate_selection.py b/sklearn/feature_selection/univariate_selection.py
index 7e34ca2356b65..057d5b4980033 100644
--- a/sklearn/feature_selection/univariate_selection.py
+++ b/sklearn/feature_selection/univariate_selection.py
@@ -496,8 +496,10 @@ def _get_support_mask(self):
 
         alpha = self.alpha
         sv = np.sort(self.pvalues_)
-        threshold = sv[sv < alpha * np.arange(len(self.pvalues_))].max()
-        return self.pvalues_ <= threshold
+        selected = sv[sv < alpha * np.arange(len(self.pvalues_))]
+        if selected.size == 0:
+            return np.zeros_like(self.pvalues_, dtype=bool)
+        return self.pvalues_ <= selected.max()
 
 
 class SelectFwe(_BaseFilter):