diff --git a/doc/source/whatsnew/v1.0.2.rst b/doc/source/whatsnew/v1.0.2.rst
index d00a418af3ddb..c9521cd7fb75c 100644
--- a/doc/source/whatsnew/v1.0.2.rst
+++ b/doc/source/whatsnew/v1.0.2.rst
@@ -92,6 +92,7 @@ Bug fixes
 - Fixed bug in setting values using a slice indexer with string dtype (:issue:`31772`)
 - Fixed bug where :meth:`pandas.core.groupby.GroupBy.first` and :meth:`pandas.core.groupby.GroupBy.last` would raise a ``TypeError`` when groups contained ``pd.NA`` in a column of object dtype (:issue:`32123`)
 - Fix bug in :meth:`Series.convert_dtypes` for series with mix of integers and strings (:issue:`32117`)
+- Fixed bug where :meth:`DataFrameGroupBy.mean`, :meth:`DataFrameGroupBy.median`, :meth:`DataFrameGroupBy.var`, and :meth:`DataFrameGroupBy.std` would raise a ``TypeError`` on ``Int64`` dtype columns (:issue:`32219`)
 
 **Strings**
 
diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index d346a0ccbcd3f..97f73966dda8a 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -1080,7 +1080,7 @@ def _cython_agg_blocks(
                         result = type(block.values)._from_sequence(
                             result.ravel(), dtype=block.values.dtype
                         )
-                    except ValueError:
+                    except (ValueError, TypeError):
                         # reshape to be valid for non-Extension Block
                         result = result.reshape(1, -1)
 
diff --git a/pandas/tests/groupby/test_function.py b/pandas/tests/groupby/test_function.py
index 1ecff003b545b..3f7b0d46faf5d 100644
--- a/pandas/tests/groupby/test_function.py
+++ b/pandas/tests/groupby/test_function.py
@@ -1563,3 +1563,34 @@ def test_groupby_mean_no_overflow():
         }
     )
     assert df.groupby("user")["connections"].mean()["A"] == 3689348814740003840
+
+
+@pytest.mark.parametrize(
+    "values",
+    [
+        {
+            "a": [1, 1, 1, 2, 2, 2, 3, 3, 3],
+            "b": [1, pd.NA, 2, 1, pd.NA, 2, 1, pd.NA, 2],
+        },
+        {"a": [1, 1, 2, 2, 3, 3], "b": [1, 2, 1, 2, 1, 2]},
+    ],
+)
+@pytest.mark.parametrize("function", ["mean", "median", "var"])
+def test_apply_to_nullable_integer_returns_float(values, function):
+    # https://github.com/pandas-dev/pandas/issues/32219
+    output = 0.5 if function == "var" else 1.5
+    arr = np.array([output] * 3, dtype=float)
+    idx = pd.Index([1, 2, 3], dtype=object, name="a")
+    expected = pd.DataFrame({"b": arr}, index=idx)
+
+    groups = pd.DataFrame(values, dtype="Int64").groupby("a")
+
+    result = getattr(groups, function)()
+    tm.assert_frame_equal(result, expected)
+
+    result = groups.agg(function)
+    tm.assert_frame_equal(result, expected)
+
+    result = groups.agg([function])
+    expected.columns = MultiIndex.from_tuples([("b", function)])
+    tm.assert_frame_equal(result, expected)