diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index 039a86da0541e..32171ae5a9e66 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -295,7 +295,7 @@ I/O
 - Bug in :meth:`DataFrame.info` where a new line at the end of the output is omitted when called on an empty :class:`DataFrame` (:issue:`45494`)
 - Bug in :func:`read_csv` not recognizing line break for ``on_bad_lines="warn"`` for ``engine="c"`` (:issue:`41710`)
 - Bug in :func:`read_parquet` when ``engine="pyarrow"`` which caused partial write to disk when column of unsupported datatype was passed (:issue:`44914`)
--
+- Bug in :func:`DataFrame.to_excel` and :class:`ExcelWriter` would raise when writing an empty DataFrame to a ``.ods`` file (:issue:`45793`)
 
 Period
 ^^^^^^
diff --git a/pandas/io/excel/_odswriter.py b/pandas/io/excel/_odswriter.py
index 9069a37ccb5af..77e75b13f968c 100644
--- a/pandas/io/excel/_odswriter.py
+++ b/pandas/io/excel/_odswriter.py
@@ -132,8 +132,9 @@ def write_cells(
             tc.addElement(p)
 
         # add all rows to the sheet
-        for row_nr in range(max(rows.keys()) + 1):
-            wks.addElement(rows[row_nr])
+        if len(rows) > 0:
+            for row_nr in range(max(rows.keys()) + 1):
+                wks.addElement(rows[row_nr])
 
     def _make_table_cell_attributes(self, cell) -> dict[str, int | str]:
         """Convert cell attributes to OpenDocument attributes
diff --git a/pandas/tests/io/excel/test_writers.py b/pandas/tests/io/excel/test_writers.py
index 4fa9a645c83a2..eb860bb49250f 100644
--- a/pandas/tests/io/excel/test_writers.py
+++ b/pandas/tests/io/excel/test_writers.py
@@ -1244,6 +1244,23 @@ def test_if_sheet_exists_raises(self, ext):
             with pytest.raises(ValueError, match=re.escape(msg)):
                 ExcelWriter(f, if_sheet_exists="replace")
 
+    def test_excel_writer_empty_frame(self, engine, ext):
+        # GH#45793
+        with tm.ensure_clean(ext) as path:
+            with ExcelWriter(path, engine=engine) as writer:
+                DataFrame().to_excel(writer)
+            result = pd.read_excel(path)
+            expected = DataFrame()
+            tm.assert_frame_equal(result, expected)
+
+    def test_to_excel_empty_frame(self, engine, ext):
+        # GH#45793
+        with tm.ensure_clean(ext) as path:
+            DataFrame().to_excel(path, engine=engine)
+            result = pd.read_excel(path)
+            expected = DataFrame()
+            tm.assert_frame_equal(result, expected)
+
 
 class TestExcelWriterEngineTests:
     @pytest.mark.parametrize(