diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index 76f6e864a174f..fa95ad06bd7ca 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -863,6 +863,7 @@ I/O
 - Bug in :func:`read_csv` not respecting a specified converter to index columns in all cases (:issue:`40589`)
 - 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`)
+- Bug in :func:`read_excel` raising uncontrolled ``IndexError`` when ``header`` references non-existing rows (:issue:`43143`)
 - Bug in :func:`read_html` where elements surrounding ``<br>`` were joined without a space between them (:issue:`29528`)
 - Bug in :func:`read_csv` when data is longer than header leading to issues with callables in ``usecols`` expecting strings (:issue:`46997`)
 - Bug in Parquet roundtrip for Interval dtype with ``datetime64[ns]`` subtype (:issue:`45881`)
diff --git a/pandas/io/excel/_base.py b/pandas/io/excel/_base.py
index d20f347e54d6b..24b881bda4805 100644
--- a/pandas/io/excel/_base.py
+++ b/pandas/io/excel/_base.py
@@ -774,6 +774,12 @@ def parse(
                         assert isinstance(skiprows, int)
                         row += skiprows
 
+                    if row > len(data) - 1:
+                        raise ValueError(
+                            f"header index {row} exceeds maximum index "
+                            f"{len(data) - 1} of data.",
+                        )
+
                     data[row], control_row = fill_mi_header(data[row], control_row)
 
                     if index_col is not None:
diff --git a/pandas/tests/io/data/excel/df_header_oob.xlsx b/pandas/tests/io/data/excel/df_header_oob.xlsx
new file mode 100644
index 0000000000000..1e26091cd2ace
Binary files /dev/null and b/pandas/tests/io/data/excel/df_header_oob.xlsx differ
diff --git a/pandas/tests/io/excel/test_readers.py b/pandas/tests/io/excel/test_readers.py
index f6c60b11cc8ff..4ca34bec0a7d9 100644
--- a/pandas/tests/io/excel/test_readers.py
+++ b/pandas/tests/io/excel/test_readers.py
@@ -1556,6 +1556,12 @@ def test_excel_read_binary_via_read_excel(self, read_ext, engine):
         expected = pd.read_excel("test1" + read_ext, engine=engine)
         tm.assert_frame_equal(result, expected)
 
+    def test_read_excel_header_index_out_of_range(self, engine):
+        # GH#43143
+        with open("df_header_oob.xlsx", "rb") as f:
+            with pytest.raises(ValueError, match="exceeds maximum"):
+                pd.read_excel(f, header=[0, 1])
+
     @pytest.mark.parametrize("filename", ["df_empty.xlsx", "df_equals.xlsx"])
     def test_header_with_index_col(self, filename):
         # GH 33476