diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 5e95cd6e5ee10..40ae4099532d0 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -753,6 +753,8 @@ Groupby/resample/rolling
 - Bug in :class:`core.window.ewm.ExponentialMovingWindow` when calling ``__getitem__`` would not retain ``com``, ``span``, ``alpha`` or ``halflife`` attributes  (:issue:`40164`)
 - :class:`core.window.ewm.ExponentialMovingWindow` now raises a ``NotImplementedError`` when specifying ``times`` with ``adjust=False`` due to an incorrect calculation (:issue:`40098`)
 - Bug in :meth:`Series.asfreq` and :meth:`DataFrame.asfreq` dropping rows when the index is not sorted (:issue:`39805`)
+- Bug in :class:`SeriesGroupBy` and :class:`DataFrameGroupBy` raising ``ValueError`` when using methods ``any`` and ``all`` with ``ExtensionDType`` columns holding ``NA`` even with ``skipna=True`` (:issue:`40585`)
+-
 
 Reshaping
 ^^^^^^^^^
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index a6c3cb3ff5d0b..bbb35c83fc6fa 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -1414,14 +1414,17 @@ def _obj_1d_constructor(self) -> Type[Series]:
         return self.obj._constructor
 
     @final
-    def _bool_agg(self, val_test, skipna):
+    def _bool_agg(self, val_test, skipna: bool):
         """
         Shared func to call any / all Cython GroupBy implementations.
         """
 
-        def objs_to_bool(vals: np.ndarray) -> Tuple[np.ndarray, Type]:
+        def objs_to_bool(vals: ArrayLike) -> Tuple[np.ndarray, Type]:
             if is_object_dtype(vals):
                 vals = np.array([bool(x) for x in vals])
+            elif isinstance(vals, ExtensionArray):
+                vals = vals.to_numpy(dtype=bool, na_value=np.nan)
+                vals = vals.astype(bool)
             else:
                 vals = vals.astype(bool)
 
diff --git a/pandas/tests/groupby/test_function.py b/pandas/tests/groupby/test_function.py
index 515774eae009b..e16d2e0f2dd0a 100644
--- a/pandas/tests/groupby/test_function.py
+++ b/pandas/tests/groupby/test_function.py
@@ -76,6 +76,35 @@ def test_groupby_bool_aggs(agg_func, skipna, vals):
     tm.assert_frame_equal(result, exp_df)
 
 
+@pytest.mark.parametrize("bool_agg_func", ["any", "all"])
+@pytest.mark.parametrize("skipna", [True, False])
+def test_bool_aggs_dup_column_labels(bool_agg_func, skipna):
+    # 21668
+    df = DataFrame([[True, True]], columns=["a", "a"])
+    grp_by = df.groupby([0])
+    result = getattr(grp_by, bool_agg_func)(skipna=skipna)
+
+    expected = df
+    tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize("bool_agg_func", ["any", "all"])
+@pytest.mark.parametrize("dtype", ["Int64", "Float64", "boolean"])
+@pytest.mark.parametrize("group_by_frame", [True, False])
+def test_bool_aggs_ea_skipna(bool_agg_func, dtype, group_by_frame):
+    # GH-40585
+    df = DataFrame({"grp": [1, 1], "val": pd.array([pd.NA, 1], dtype=dtype)})
+    if group_by_frame:
+        grouped = df.groupby("grp")
+        expected = DataFrame({"val": [True]}, index=Index([1], name="grp"))
+    else:
+        grouped = df["val"].groupby(df["grp"])
+        expected = Series([True], index=Index([1], name="grp"), name="val")
+
+    result = grouped.agg(bool_agg_func, skipna=True)
+    tm.assert_equal(result, expected)
+
+
 def test_max_min_non_numeric():
     # #2700
     aa = DataFrame({"nn": [11, 11, 22, 22], "ii": [1, 2, 3, 4], "ss": 4 * ["mama"]})
diff --git a/pandas/tests/groupby/test_groupby.py b/pandas/tests/groupby/test_groupby.py
index de508b8cd78ec..6c51e32fa9a78 100644
--- a/pandas/tests/groupby/test_groupby.py
+++ b/pandas/tests/groupby/test_groupby.py
@@ -1978,17 +1978,6 @@ def test_groupby_duplicate_index():
     tm.assert_series_equal(result, expected)
 
 
-@pytest.mark.parametrize("bool_agg_func", ["any", "all"])
-def test_bool_aggs_dup_column_labels(bool_agg_func):
-    # 21668
-    df = DataFrame([[True, True]], columns=["a", "a"])
-    grp_by = df.groupby([0])
-    result = getattr(grp_by, bool_agg_func)()
-
-    expected = df
-    tm.assert_frame_equal(result, expected)
-
-
 @pytest.mark.parametrize(
     "idx", [Index(["a", "a"]), MultiIndex.from_tuples((("a", "a"), ("a", "a")))]
 )