diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index cd2b8a8055e68..20a25c9d4dd79 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -1128,6 +1128,7 @@ ExtensionArray
 - Fixed bug where :meth:`StringArray.memory_usage` was not implemented (:issue:`33963`)
 - Fixed bug where :meth:`DataFrameGroupBy` would ignore the ``min_count`` argument for aggregations on nullable boolean dtypes (:issue:`34051`)
 - Fixed bug that `DataFrame(columns=.., dtype='string')` would fail (:issue:`27953`, :issue:`33623`)
+- Fixed bug where :meth:`DataFrame.min` and :meth:`DataFrame.max` with Int64 columns casts to float64 (:issue:`32651`)
 
 Other
 ^^^^^
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index f6ea6f51d88a8..9e14773738faf 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -8508,7 +8508,9 @@ def _get_data(axis_matters):
                 raise NotImplementedError(msg)
             return data
 
-        if numeric_only is not None and axis in [0, 1]:
+        is_numeric = self._mgr.blocks and all(b.is_numeric for b in self._mgr.blocks)
+
+        if (is_numeric or numeric_only is not None) and axis is not None:
             df = self
             if numeric_only is True:
                 df = _get_data(axis_matters=True)
diff --git a/pandas/tests/frame/test_analytics.py b/pandas/tests/frame/test_analytics.py
index db8bb5ca3c437..4d58f2677df56 100644
--- a/pandas/tests/frame/test_analytics.py
+++ b/pandas/tests/frame/test_analytics.py
@@ -912,6 +912,19 @@ def test_mean_extensionarray_numeric_only_true(self):
         expected = pd.DataFrame(arr).mean()
         tm.assert_series_equal(result, expected)
 
+    @pytest.mark.parametrize("numeric_only", [True, False, None])
+    @pytest.mark.parametrize("method", ["min", "max"])
+    def test_minmax_extensionarray(self, method, numeric_only):
+        # https://github.com/pandas-dev/pandas/issues/32651
+        int64_info = np.iinfo("int64")
+        ser = Series([int64_info.max, None, int64_info.min], dtype=pd.Int64Dtype())
+        df = DataFrame({"Int64": ser})
+        result = getattr(df, method)(numeric_only=numeric_only)
+        expected = Series(
+            [getattr(int64_info, method)], index=pd.Index(["Int64"], dtype="object")
+        )
+        tm.assert_series_equal(result, expected)
+
     def test_stats_mixed_type(self, float_string_frame):
         # don't blow up
         float_string_frame.std(1)