diff --git a/doc/whats_new/v0.23.rst b/doc/whats_new/v0.23.rst
index 750336a81e109..32716cb9eb694 100644
--- a/doc/whats_new/v0.23.rst
+++ b/doc/whats_new/v0.23.rst
@@ -124,6 +124,11 @@ Changelog
   for datasets with large vocabularies combined with ``min_df`` or ``max_df``.
   :pr:`15834` by :user:`Santiago M. Mola <smola>`.
 
+
+- |Enhancement| Added support for multioutput data in
+  :class:`feature_selection.RFE` and :class:`feature_selection.RFECV`.
+  :pr:`16103` by :user:`Divyaprabha M <divyaprabha123>`.
+
 :mod:`sklearn.gaussian_process`
 ...............................
 
diff --git a/sklearn/feature_selection/_rfe.py b/sklearn/feature_selection/_rfe.py
index 12e99175c9d61..91312c7dc80f9 100644
--- a/sklearn/feature_selection/_rfe.py
+++ b/sklearn/feature_selection/_rfe.py
@@ -156,7 +156,8 @@ def _fit(self, X, y, step_score=None):
 
         tags = self._get_tags()
         X, y = check_X_y(X, y, "csc", ensure_min_features=2,
-                         force_all_finite=not tags.get('allow_nan', True))
+                         force_all_finite=not tags.get('allow_nan', True),
+                         multi_output=True)
         # Initialization
         n_features = X.shape[1]
         if self.n_features_to_select is None:
@@ -489,8 +490,10 @@ def fit(self, X, y, groups=None):
             train/test set. Only used in conjunction with a "Group" :term:`cv`
             instance (e.g., :class:`~sklearn.model_selection.GroupKFold`).
         """
-        X, y = check_X_y(X, y, "csr", ensure_min_features=2,
-                         force_all_finite=False)
+        tags = self._get_tags()
+        X, y = check_X_y(X, y, "csc", ensure_min_features=2,
+                         force_all_finite=not tags.get('allow_nan', True),
+                         multi_output=True)
 
         # Initialization
         cv = check_cv(self.cv, y, is_classifier(self.estimator))
diff --git a/sklearn/feature_selection/tests/test_rfe.py b/sklearn/feature_selection/tests/test_rfe.py
index ccd3c0a1b0e83..654675e677a11 100644
--- a/sklearn/feature_selection/tests/test_rfe.py
+++ b/sklearn/feature_selection/tests/test_rfe.py
@@ -395,3 +395,15 @@ def test_rfe_allow_nan_inf_in_x(cv):
         rfe = RFE(estimator=clf)
     rfe.fit(X, y)
     rfe.transform(X)
+
+
+@pytest.mark.parametrize('ClsRFE', [
+    RFE,
+    RFECV
+    ])
+def test_multioutput(ClsRFE):
+    X = np.random.normal(size=(10, 3))
+    y = np.random.randint(2, size=(10, 2))
+    clf = RandomForestClassifier(n_estimators=5)
+    rfe_test = ClsRFE(clf)
+    rfe_test.fit(X, y)