diff --git a/sklearn/feature_selection/base.py b/sklearn/feature_selection/base.py
index 3067d6ef31bc1..a9239e7fc9a8c 100644
--- a/sklearn/feature_selection/base.py
+++ b/sklearn/feature_selection/base.py
@@ -72,7 +72,11 @@ def transform(self, X):
         X_r : array of shape [n_samples, n_selected_features]
             The input samples with only the selected features.
         """
-        X = check_array(X, accept_sparse='csr')
+        return self._transform(X)
+
+    def _transform(self, X, force_all_finite=True):
+        X = check_array(X, force_all_finite=force_all_finite,
+                        accept_sparse='csr')
         mask = self.get_support()
         if not mask.any():
             warn("No features were selected: either the data is"
diff --git a/sklearn/feature_selection/from_model.py b/sklearn/feature_selection/from_model.py
index 657259f39ea17..42618a19e3b54 100644
--- a/sklearn/feature_selection/from_model.py
+++ b/sklearn/feature_selection/from_model.py
@@ -143,6 +143,9 @@ def _get_support_mask(self):
         threshold = _calculate_threshold(estimator, scores, self.threshold)
         return scores >= threshold
 
+    def transform(self, X):
+        return self._transform(X, False)
+
     def fit(self, X, y=None, **fit_params):
         """Fit the SelectFromModel meta-transformer.
 
diff --git a/sklearn/feature_selection/tests/test_from_model.py b/sklearn/feature_selection/tests/test_from_model.py
index 6efec43dce37b..d0fde777b13c8 100644
--- a/sklearn/feature_selection/tests/test_from_model.py
+++ b/sklearn/feature_selection/tests/test_from_model.py
@@ -1,5 +1,6 @@
 import numpy as np
 
+from sklearn.impute import SimpleImputer
 from sklearn.utils.testing import assert_true
 from sklearn.utils.testing import assert_false
 from sklearn.utils.testing import assert_equal
@@ -198,3 +199,17 @@ def test_threshold_without_refitting():
     # Set a higher threshold to filter out more features.
     model.threshold = "1.0 * mean"
     assert_greater(X_transform.shape[1], model.transform(data).shape[1])
+
+
+def test_transform_accepts_infinite_data():
+    # Test that transform doesn't check for np.inf and np.nan values.
+    est = SimpleImputer(strategy='mean', missing_values='NaN')
+    model = SelectFromModel(estimator=est)
+    data[2, :] = np.nan
+    model.fit(data, y)
+
+    X_len = len(model.get_support())
+    X = np.arange(X_len).reshape(1, X_len)
+    X.fill(np.inf)
+
+    model.transform(X)