diff --git a/sklearn/linear_model/coordinate_descent.py b/sklearn/linear_model/coordinate_descent.py
index 2a38eb65831f6..b9257026551f9 100644
--- a/sklearn/linear_model/coordinate_descent.py
+++ b/sklearn/linear_model/coordinate_descent.py
@@ -1150,7 +1150,7 @@ def fit(self, X, y):
         cv = check_cv(self.cv)
 
         # Compute path for all folds and compute MSE to get the best alpha
-        folds = list(cv.split(X))
+        folds = list(cv.split(X, y))
         best_mse = np.inf
 
         # We do a double for loop folded in one, in order to be able to
diff --git a/sklearn/linear_model/tests/test_coordinate_descent.py b/sklearn/linear_model/tests/test_coordinate_descent.py
index 13f3a999d8434..8c3ff10bcfd2e 100644
--- a/sklearn/linear_model/tests/test_coordinate_descent.py
+++ b/sklearn/linear_model/tests/test_coordinate_descent.py
@@ -175,6 +175,24 @@ def test_lasso_cv():
     assert_greater(clf.score(X_test, y_test), 0.99)
 
 
+def test_lasso_cv_with_some_model_selection():
+    from sklearn.pipeline import make_pipeline
+    from sklearn.preprocessing import StandardScaler
+    from sklearn.model_selection import StratifiedKFold
+    from sklearn import datasets
+    from sklearn.linear_model import LassoCV
+
+    diabetes = datasets.load_diabetes()
+    X = diabetes.data
+    y = diabetes.target
+
+    pipe = make_pipeline(
+        StandardScaler(),
+        LassoCV(cv=StratifiedKFold(n_splits=5))
+    )
+    pipe.fit(X, y)
+
+
 def test_lasso_cv_positive_constraint():
     X, y, X_test, y_test = build_dataset()
     max_iter = 500