BUG Avoid IndexError on writing empty (row) MI df to excel (GH19543)

doc/source/whatsnew/v1.5.0.rst

@@ -872,6 +872,7 @@ I/O
 - Bug in :func:`read_sas` returned ``None`` rather than an empty DataFrame for SAS7BDAT files with zero rows (:issue:`18198`)
 - Bug in :class:`StataWriter` where value labels were always written with default encoding (:issue:`46750`)
 - Bug in :class:`StataWriterUTF8` where some valid characters were removed from variable names (:issue:`47276`)
+- Bug in :meth:`DataFrame.to_excel` when writing an empty dataframe with :class:`MultiIndex` (:issue:`19543`)
 
 Period
 ^^^^^^

pandas/io/formats/excel.py

@@ -634,7 +634,7 @@ def _format_header_regular(self) -> Iterable[ExcelCell]:
             if self.index:
                 coloffset = 1
                 if isinstance(self.df.index, MultiIndex):
-                    coloffset = len(self.df.index[0])
+                    coloffset = len(self.df.index.names)
 
             colnames = self.columns
             if self._has_aliases:

pandas/tests/io/excel/test_writers.py

@@ -838,6 +838,19 @@ def test_to_excel_multiindex_no_write_index(self, path):
         # Test that it is the same as the initial frame.
         tm.assert_frame_equal(frame1, frame3)
 
+    def test_to_excel_empty_multiindex(self, path):
+        # GH 19543.
+        expected = DataFrame([], columns=[0, 1, 2])
+
+        df = DataFrame([], index=MultiIndex.from_tuples([], names=[0, 1]), columns=[2])
+        df.to_excel(path, "test1")
+
+        with ExcelFile(path) as reader:
+            result = pd.read_excel(reader, sheet_name="test1")
+        tm.assert_frame_equal(
+            result, expected, check_index_type=False, check_dtype=False
+        )
+
     def test_to_excel_float_format(self, path):
         df = DataFrame(
             [[0.123456, 0.234567, 0.567567], [12.32112, 123123.2, 321321.2]],