diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index cd0714838a3f1..2e188ec5a9af5 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -184,7 +184,7 @@ Groupby/resample/rolling
 Reshaping
 ^^^^^^^^^
 
--
+- Bug in :meth:`DataFrame.drop` when passing empty :class:`DatetimeIndex` or ``list`` (:issue:`27994`)
 -
 
 Sparse
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 1a5b36b07e93c..93bad6fa94277 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -3916,6 +3916,9 @@ def drop(
 
         for axis, labels in axes.items():
             if labels is not None:
+                # Check for empty Index, GH 27994
+                if is_list_like(labels) and not len(labels):
+                    continue
                 obj = obj._drop_axis(labels, axis, level=level, errors=errors)
 
         if inplace:
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 2dbd592fc6787..9022fa9ee69e7 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -4720,6 +4720,10 @@ def get_indexer_non_unique(self, target):
             return pself.get_indexer_non_unique(ptarget)
 
         if self.is_all_dates:
+            # If `target` doesn't consist of dates, `target.asi8` will return
+            # None, which will raise TypeError. GH 27994
+            if not target.is_all_dates:
+                raise KeyError("{} not found in axis".format(target.to_numpy()))
             tgt_values = target.asi8
         else:
             tgt_values = target._ndarray_values
diff --git a/pandas/tests/frame/test_axis_select_reindex.py b/pandas/tests/frame/test_axis_select_reindex.py
index 1ef10ea5857d0..901cdfbe1a032 100644
--- a/pandas/tests/frame/test_axis_select_reindex.py
+++ b/pandas/tests/frame/test_axis_select_reindex.py
@@ -117,6 +117,32 @@ def test_drop(self):
         df.drop(labels=df[df.b > 0].index, inplace=True)
         assert_frame_equal(df, expected)
 
+    def test_drop_empty_index(self):
+        # GH 27994
+        df = pd.DataFrame(
+            {"a": [0, 1]},
+            index=[pd.Timestamp("2019-01-01"), pd.Timestamp("2019-01-01")],
+        )
+        result_empty_list = df.drop([])
+        assert_frame_equal(result_empty_list, df)
+
+        result_empty_array = df.drop(np.array([]))
+        assert_frame_equal(result_empty_array, df)
+
+        result_empty_index = df.drop(df[:0])
+        assert_frame_equal(result_empty_index, df)
+
+    @pytest.mark.parametrize("labels", ["a", ["a"]])
+    def test_drop_empty_index_str(self, labels):
+        # Passing str to DataFrame.drop() for dataframe with DatetimeIndex
+        # should raise KeyError, GH 27994
+        df = pd.DataFrame(
+            {"a": [0, 1]},
+            index=[pd.Timestamp("2019-01-01"), pd.Timestamp("2019-01-01")],
+        )
+        with pytest.raises(KeyError, match="not found in axis"):
+            df.drop(labels)
+
     def test_drop_multiindex_not_lexsorted(self):
         # GH 11640