diff --git a/pandas/tests/groupby/test_function.py b/pandas/tests/groupby/test_function.py
index 6f19ec40c2520..e693962e57ac3 100644
--- a/pandas/tests/groupby/test_function.py
+++ b/pandas/tests/groupby/test_function.py
@@ -85,6 +85,24 @@ def test_max_min_non_numeric():
     assert "ss" in result
 
 
+def test_min_date_with_nans():
+    # GH26321
+    dates = pd.to_datetime(
+        pd.Series(["2019-05-09", "2019-05-09", "2019-05-09"]), format="%Y-%m-%d"
+    ).dt.date
+    df = pd.DataFrame({"a": [np.nan, "1", np.nan], "b": [0, 1, 1], "c": dates})
+
+    result = df.groupby("b", as_index=False)["c"].min()["c"]
+    expected = pd.to_datetime(
+        pd.Series(["2019-05-09", "2019-05-09"], name="c"), format="%Y-%m-%d"
+    ).dt.date
+    tm.assert_series_equal(result, expected)
+
+    result = df.groupby("b")["c"].min()
+    expected.index.name = "b"
+    tm.assert_series_equal(result, expected)
+
+
 def test_intercept_builtin_sum():
     s = Series([1.0, 2.0, np.nan, 3.0])
     grouped = s.groupby([0, 1, 2, 2])