BUG: Convert output type in Excel for MultiIndex with period levels

pandas/io/formats/excel.py

@@ -37,6 +37,7 @@
     DataFrame,
     Index,
     MultiIndex,
+    Period,
     PeriodIndex,
 )
 import pandas.core.common as com
@@ -825,6 +826,9 @@ def _format_hierarchical_rows(self) -> Iterable[ExcelCell]:
                         allow_fill=levels._can_hold_na,
                         fill_value=levels._na_value,
                     )
+                    # GH#60099
+                    if isinstance(values[0], Period):
+                        values = values.to_timestamp()
 
                     for i, span_val in spans.items():
                         mergestart, mergeend = None, None
@@ -849,6 +853,10 @@ def _format_hierarchical_rows(self) -> Iterable[ExcelCell]:
                 # Format hierarchical rows with non-merged values.
                 for indexcolvals in zip(*self.df.index):
                     for idx, indexcolval in enumerate(indexcolvals):
+                        # GH#60099
+                        if isinstance(indexcolval, Period):
+                            indexcolval = indexcolval.to_timestamp()
+
                         yield CssExcelCell(
                             row=self.rowcounter + idx,
                             col=gcolidx,

pandas/tests/io/excel/test_style.py

@@ -9,6 +9,9 @@
 
 from pandas import (
     DataFrame,
+    MultiIndex,
+    Period,
+    period_range,
     read_excel,
 )
 import pandas._testing as tm
@@ -333,3 +336,22 @@ def test_styler_to_s3(s3_public_bucket, s3so):
             f"s3://{mock_bucket_name}/{target_file}", index_col=0, storage_options=s3so
         )
         tm.assert_frame_equal(result, df)
+
+
+@pytest.mark.parametrize("merge_cells", [True, False])
+def test_format_hierarchical_rows_periodindex(merge_cells):
+    # GH#60099
+    df = DataFrame(
+        {"A": [1, 2]},
+        index=MultiIndex.from_arrays(
+            [period_range("2023-01", "2023-02", freq="M"), ["X", "Y"]],
+            names=["date", "category"],
+        ),
+    )
+    formatter = ExcelFormatter(df, merge_cells=merge_cells)
+    formatted_cells = list(formatter._format_hierarchical_rows())
+
+    for cell in formatted_cells:
+        assert not isinstance(
+            cell.val, Period
+        ), "Period should be converted to Timestamp"

pandas/tests/io/excel/test_writers.py

@@ -25,6 +25,7 @@
     MultiIndex,
     date_range,
     option_context,
+    period_range,
 )
 import pandas._testing as tm
 
@@ -1549,3 +1550,27 @@ def test_subclass_attr(klass):
     attrs_base = {name for name in dir(ExcelWriter) if not name.startswith("_")}
     attrs_klass = {name for name in dir(klass) if not name.startswith("_")}
     assert not attrs_base.symmetric_difference(attrs_klass)
+
+
+@pytest.mark.parametrize("merge_cells", [True, False])
+def test_excel_round_trip_with_periodindex(merge_cells, engine):
+    # GH#60099
+    df = DataFrame(
+        {"A": [1, 2]},
+        index=MultiIndex.from_arrays(
+            [period_range("2023-01", "2023-02", freq="M"), ["X", "Y"]],
+            names=["date", "category"],
+        ),
+    )
+
+    with BytesIO() as buffer:
+        with ExcelWriter(buffer) as writer:
+            df.to_excel(writer, merge_cells=merge_cells)
+
+        buffer.seek(0)
+        result_df = pd.read_excel(buffer, index_col=[0, 1])
+        result_df.index = result_df.index.set_levels(
+            [result_df.index.levels[0].to_period("M"), result_df.index.levels[1]]
+        )
+
+    tm.assert_frame_equal(df, result_df)