diff --git a/doc/source/whatsnew/v2.1.0.rst b/doc/source/whatsnew/v2.1.0.rst
index d0dae450735a3..eab1da837a640 100644
--- a/doc/source/whatsnew/v2.1.0.rst
+++ b/doc/source/whatsnew/v2.1.0.rst
@@ -643,6 +643,7 @@ Other
 - Bug in :meth:`DataFrame.reindex` with a ``fill_value`` that should be inferred with a :class:`ExtensionDtype` incorrectly inferring ``object`` dtype (:issue:`52586`)
 - Bug in :meth:`DataFrame.shift` and :meth:`Series.shift` and :meth:`DataFrameGroupBy.shift` when passing both "freq" and "fill_value" silently ignoring "fill_value" instead of raising ``ValueError`` (:issue:`53832`)
 - Bug in :meth:`DataFrame.shift` with ``axis=1`` on a :class:`DataFrame` with a single :class:`ExtensionDtype` column giving incorrect results (:issue:`53832`)
+- Bug in :meth:`GroupBy.first` and :meth:`GroupBy.last` where an empty group would return ``np.nan`` instead of a an ExtensionArray's NA value (:issue:`39098`)
 - Bug in :meth:`Index.sort_values` when a ``key`` is passed (:issue:`52764`)
 - Bug in :meth:`Series.align`, :meth:`DataFrame.align`, :meth:`Series.reindex`, :meth:`DataFrame.reindex`, :meth:`Series.interpolate`, :meth:`DataFrame.interpolate`, incorrectly failing to raise with method="asfreq" (:issue:`53620`)
 - Bug in :meth:`Series.argsort` failing to raise when an invalid ``axis`` is passed (:issue:`54257`)
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index 8d8302826462e..f70fc4303f938 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -3279,7 +3279,7 @@ def first(x: Series):
                 """Helper function for first item that isn't NA."""
                 arr = x.array[notna(x.array)]
                 if not len(arr):
-                    return np.nan
+                    return x.array.dtype.na_value
                 return arr[0]
 
             if isinstance(obj, DataFrame):
@@ -3338,7 +3338,7 @@ def last(x: Series):
                 """Helper function for last item that isn't NA."""
                 arr = x.array[notna(x.array)]
                 if not len(arr):
-                    return np.nan
+                    return x.array.dtype.na_value
                 return arr[-1]
 
             if isinstance(obj, DataFrame):
diff --git a/pandas/tests/extension/json/test_json.py b/pandas/tests/extension/json/test_json.py
index 0920e70142446..fb2208b304f9e 100644
--- a/pandas/tests/extension/json/test_json.py
+++ b/pandas/tests/extension/json/test_json.py
@@ -356,10 +356,6 @@ def test_groupby_extension_no_sort(self):
         """
         super().test_groupby_extension_no_sort()
 
-    @pytest.mark.xfail(reason="GH#39098: Converts agg result to object")
-    def test_groupby_agg_extension(self, data_for_grouping):
-        super().test_groupby_agg_extension(data_for_grouping)
-
 
 class TestArithmeticOps(BaseJSON, base.BaseArithmeticOpsTests):
     def test_arith_frame_with_scalar(self, data, all_arithmetic_operators, request):