diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index 5514265f37f05b..97fba5a8e1f381 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -401,6 +401,8 @@ Plotting
 Groupby/resample/rolling
 ^^^^^^^^^^^^^^^^^^^^^^^^
 
+-
+- Bug in :meth:`DataFrame.groupby` with multiple groups where an ``IndexError`` would be raised if any group contained all NA values (:issue:`20519`)
 - Bug in :meth:`DataFrame.rolling` not allowing for rolling over datetimes when ``axis=1`` (:issue: `28192`)
 - Bug in :meth:`DataFrame.rolling` not allowing rolling over multi-index levels (:issue: `15584`).
 - Bug in :meth:`DataFrame.rolling` not allowing rolling on monotonic decreasing time indexes (:issue: `19248`).
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 74dbcd4067ec00..dc2abfb0cb6eb7 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -1308,7 +1308,10 @@ def _get_grouper_for_level(self, mapper, level):
             # Remove unobserved levels from level_index
             level_index = level_index.take(uniques)
 
-        grouper = level_index.take(codes)
+        if len(level_index):
+            grouper = level_index.take(codes)
+        else:
+            grouper = level_index.take(codes, fill_value=True)
 
         return grouper, codes, level_index
 
diff --git a/pandas/tests/groupby/test_grouping.py b/pandas/tests/groupby/test_grouping.py
index 403f5f11ee7686..ab25d183ae3ff8 100644
--- a/pandas/tests/groupby/test_grouping.py
+++ b/pandas/tests/groupby/test_grouping.py
@@ -628,6 +628,24 @@ def test_groupby_empty(self):
         # check name
         assert s.groupby(s).grouper.names == ["name"]
 
+    def test_groupby_level_index_value_all_na(self):
+        # issue 20519
+        df = DataFrame(
+            [["x", np.nan, 10], [None, np.nan, 20]], columns=["A", "B", "C"]
+        ).set_index(["A", "B"])
+        result = df.groupby(level=["A", "B"]).sum()
+        expected = DataFrame(
+            data=[],
+            index=MultiIndex(
+                levels=[Index(["x"], dtype="object"), Index([], dtype="float64")],
+                codes=[[], []],
+                names=["A", "B"],
+            ),
+            columns=["C"],
+            dtype="int64",
+        )
+        tm.assert_frame_equal(result, expected)
+
 
 # get_group
 # --------------------------------