diff --git a/openml/datasets/dataset.py b/openml/datasets/dataset.py
index 0c065b855..122e2e697 100644
--- a/openml/datasets/dataset.py
+++ b/openml/datasets/dataset.py
@@ -628,7 +628,7 @@ def _encode_if_category(column):
                 )
         elif array_format == "dataframe":
             if scipy.sparse.issparse(data):
-                return pd.DataFrame.sparse.from_spmatrix(data, columns=attribute_names)
+                data = pd.DataFrame.sparse.from_spmatrix(data, columns=attribute_names)
         else:
             data_type = "sparse-data" if scipy.sparse.issparse(data) else "non-sparse data"
             logger.warning(
@@ -732,6 +732,7 @@ def get_data(
                 else:
                     target = [target]
             targets = np.array([True if column in target else False for column in attribute_names])
+            target_names = np.array([column for column in attribute_names if column in target])
             if np.sum(targets) > 1:
                 raise NotImplementedError(
                     "Number of requested targets %d is not implemented." % np.sum(targets)
@@ -752,11 +753,17 @@ def get_data(
             attribute_names = [att for att, k in zip(attribute_names, targets) if not k]
 
             x = self._convert_array_format(x, dataset_format, attribute_names)
-            if scipy.sparse.issparse(y):
-                y = np.asarray(y.todense()).astype(target_dtype).flatten()
-            y = y.squeeze()
-            y = self._convert_array_format(y, dataset_format, attribute_names)
+            if dataset_format == "array" and scipy.sparse.issparse(y):
+                # scikit-learn requires dense representation of targets
+                y = np.asarray(y.todense()).astype(target_dtype)
+                # dense representation of single column sparse arrays become a 2-d array
+                # need to flatten it to a 1-d array for _convert_array_format()
+                y = y.squeeze()
+            y = self._convert_array_format(y, dataset_format, target_names)
             y = y.astype(target_dtype) if dataset_format == "array" else y
+            if len(y.shape) > 1 and y.shape[1] == 1:
+                # single column targets should be 1-d for both `array` and `dataframe` formats
+                y = y.squeeze()
             data, targets = x, y
 
         return data, targets, categorical, attribute_names
diff --git a/tests/test_datasets/test_dataset.py b/tests/test_datasets/test_dataset.py
index 1aeffdbb4..e9cb86c50 100644
--- a/tests/test_datasets/test_dataset.py
+++ b/tests/test_datasets/test_dataset.py
@@ -287,7 +287,7 @@ def setUp(self):
 
         self.sparse_dataset = openml.datasets.get_dataset(4136, download_data=False)
 
-    def test_get_sparse_dataset_with_target(self):
+    def test_get_sparse_dataset_array_with_target(self):
         X, y, _, attribute_names = self.sparse_dataset.get_data(
             dataset_format="array", target="class"
         )
@@ -303,7 +303,22 @@ def test_get_sparse_dataset_with_target(self):
         self.assertEqual(len(attribute_names), 20000)
         self.assertNotIn("class", attribute_names)
 
-    def test_get_sparse_dataset(self):
+    def test_get_sparse_dataset_dataframe_with_target(self):
+        X, y, _, attribute_names = self.sparse_dataset.get_data(
+            dataset_format="dataframe", target="class"
+        )
+        self.assertIsInstance(X, pd.DataFrame)
+        self.assertIsInstance(X.dtypes[0], pd.SparseDtype)
+        self.assertEqual(X.shape, (600, 20000))
+
+        self.assertIsInstance(y, pd.Series)
+        self.assertIsInstance(y.dtypes, pd.SparseDtype)
+        self.assertEqual(y.shape, (600,))
+
+        self.assertEqual(len(attribute_names), 20000)
+        self.assertNotIn("class", attribute_names)
+
+    def test_get_sparse_dataset_array(self):
         rval, _, categorical, attribute_names = self.sparse_dataset.get_data(dataset_format="array")
         self.assertTrue(sparse.issparse(rval))
         self.assertEqual(rval.dtype, np.float32)
@@ -315,7 +330,7 @@ def test_get_sparse_dataset(self):
         self.assertEqual(len(attribute_names), 20001)
         self.assertTrue(all([isinstance(att, str) for att in attribute_names]))
 
-    def test_get_sparse_dataframe(self):
+    def test_get_sparse_dataset_dataframe(self):
         rval, *_ = self.sparse_dataset.get_data()
         self.assertIsInstance(rval, pd.DataFrame)
         np.testing.assert_array_equal(