diff --git a/pandas/io/formats/format.py b/pandas/io/formats/format.py
index ea938c924ae0c..2cf4930ebc801 100644
--- a/pandas/io/formats/format.py
+++ b/pandas/io/formats/format.py
@@ -1621,18 +1621,23 @@ def __init__(
 
     def _format_strings(self) -> list[str]:
         """we by definition have DO NOT have a TZ"""
-        values = self.values
 
+        values = self.values
         if not isinstance(values, DatetimeIndex):
             values = DatetimeIndex(values)
 
         if self.formatter is not None and callable(self.formatter):
-            return [self.formatter(x) for x in values]
+            fmt_values = np.array([self.formatter(x) for x in values])
+        else:
+            fmt_values = values._data._format_native_types(
+                na_rep=self.nat_rep, date_format=self.date_format
+            )
 
-        fmt_values = values._data._format_native_types(
-            na_rep=self.nat_rep, date_format=self.date_format
-        )
-        return fmt_values.tolist()
+        if fmt_values.ndim > 1:
+            nested_formatter = GenericArrayFormatter(fmt_values)
+            return list(nested_formatter.get_result())
+
+        return list(fmt_values)
 
 
 class ExtensionArrayFormatter(GenericArrayFormatter):
@@ -1811,9 +1816,12 @@ def _format_strings(self) -> list[str]:
         formatter = self.formatter or get_format_datetime64(
             ido, date_format=self.date_format
         )
-        fmt_values = [formatter(x) for x in values]
+        fmt_values = np.frompyfunc(formatter, 1, 1)(values)
+        if fmt_values.ndim > 1:
+            nested_formatter = GenericArrayFormatter(fmt_values)
+            return list(nested_formatter.get_result())
 
-        return fmt_values
+        return list(fmt_values)
 
 
 class Timedelta64Formatter(GenericArrayFormatter):
diff --git a/pandas/tests/io/formats/test_format.py b/pandas/tests/io/formats/test_format.py
index adcaeba5cfd8d..71531ccf4e02a 100644
--- a/pandas/tests/io/formats/test_format.py
+++ b/pandas/tests/io/formats/test_format.py
@@ -3158,6 +3158,97 @@ def format_func(x):
         result = formatter.get_result()
         assert result == ["10:10", "12:12"]
 
+    def test_datetime64formatter_2d_array(self):
+        # GH#38390
+        x = date_range("2018-01-01", periods=10, freq="H").to_numpy()
+
+        formatter = fmt.Datetime64Formatter(x.reshape((5, 2)))
+        result = formatter.get_result()
+        assert len(result) == 5
+        assert result[0].strip() == "[2018-01-01 00:00:00, 2018-01-01 01:00:00]"
+        assert result[4].strip() == "[2018-01-01 08:00:00, 2018-01-01 09:00:00]"
+
+        formatter = fmt.Datetime64Formatter(x.reshape((2, 5)))
+        result = formatter.get_result()
+        assert len(result) == 2
+        assert result[0].strip() == "[2018-01-01 00:00:00, 2018-01-01 01:00:00, 201..."
+        assert result[1].strip() == "[2018-01-01 05:00:00, 2018-01-01 06:00:00, 201..."
+
+    def test_datetime64formatter_3d_array(self):
+        # GH#38390
+        x = date_range("2018-01-01", periods=10, freq="H").to_numpy()
+
+        formatter = fmt.Datetime64Formatter(x.reshape((10, 1, 1)))
+        result = formatter.get_result()
+        assert len(result) == 10
+        assert result[0].strip() == "[[2018-01-01 00:00:00]]"
+        assert result[9].strip() == "[[2018-01-01 09:00:00]]"
+
+    def test_datetime64formatter_3d_array_format_func(self):
+        # GH#38390
+        x = date_range("2018-01-01", periods=24, freq="H").to_numpy()
+
+        def format_func(t):
+            return t.strftime("%H-%m")
+
+        formatter = fmt.Datetime64Formatter(x.reshape((4, 2, 3)), formatter=format_func)
+        result = formatter.get_result()
+        assert len(result) == 4
+        assert result[0].strip() == "[[00-01, 01-01, 02-01], [03-01, 04-01, 05-01]]"
+        assert result[3].strip() == "[[18-01, 19-01, 20-01], [21-01, 22-01, 23-01]]"
+
+
+class TestDatetime64TZFormatter:
+    def test_mixed(self):
+        # GH#38390
+        utc = dateutil.tz.tzutc()
+        x = Series(
+            [
+                datetime(2013, 1, 1, tzinfo=utc),
+                datetime(2013, 1, 1, 12, tzinfo=utc),
+                NaT,
+            ]
+        )
+        result = fmt.Datetime64TZFormatter(x).get_result()
+        assert len(result) == 3
+        assert result[0].strip() == "2013-01-01 00:00:00+00:00"
+        assert result[1].strip() == "2013-01-01 12:00:00+00:00"
+        assert result[2].strip() == "NaT"
+
+    def test_datetime64formatter_1d_array(self):
+        # GH#38390
+        x = date_range("2018-01-01", periods=3, freq="H", tz="US/Pacific").to_numpy()
+        formatter = fmt.Datetime64TZFormatter(x)
+        result = formatter.get_result()
+        assert len(result) == 3
+        assert result[0].strip() == "2018-01-01 00:00:00-08:00"
+        assert result[1].strip() == "2018-01-01 01:00:00-08:00"
+        assert result[2].strip() == "2018-01-01 02:00:00-08:00"
+
+    def test_datetime64formatter_2d_array(self):
+        # GH#38390
+        x = date_range("2018-01-01", periods=10, freq="H", tz="US/Pacific").to_numpy()
+        formatter = fmt.Datetime64TZFormatter(x.reshape((5, 2)))
+        result = formatter.get_result()
+        assert len(result) == 5
+        assert result[0].strip() == "[2018-01-01 00:00:00-08:00, 2018-01-01 01:00:0..."
+        assert result[4].strip() == "[2018-01-01 08:00:00-08:00, 2018-01-01 09:00:0..."
+
+    def test_datetime64formatter_2d_array_format_func(self):
+        # GH#38390
+        x = date_range("2018-01-01", periods=16, freq="H", tz="US/Pacific").to_numpy()
+
+        def format_func(t):
+            return t.strftime("%H-%m %Z")
+
+        formatter = fmt.Datetime64TZFormatter(
+            x.reshape((4, 2, 2)), formatter=format_func
+        )
+        result = formatter.get_result()
+        assert len(result) == 4
+        assert result[0].strip() == "[[00-01 PST, 01-01 PST], [02-01 PST, 03-01 PST]]"
+        assert result[3].strip() == "[[12-01 PST, 13-01 PST], [14-01 PST, 15-01 PST]]"
+
 
 class TestNaTFormatting:
     def test_repr(self):