diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 26e548f519ecd..80e5484c5f324 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -217,6 +217,7 @@ MultiIndex
 I/O
 ^^^
 
+- Bug in :func:`read_csv` raising ``IndexError`` with multiple header columns and ``index_col`` specified when file has no data rows (:issue:`38292`)
 - Bug in :func:`read_csv` not accepting ``usecols`` with different length than ``names`` for ``engine="python"`` (:issue:`16469`)
 - Bug in :func:`read_csv` raising ``TypeError`` when ``names`` and ``parse_dates`` is specified for ``engine="c"`` (:issue:`33699`)
 -
diff --git a/pandas/io/parsers.py b/pandas/io/parsers.py
index 8177741b5252d..3244b1c0f65b2 100644
--- a/pandas/io/parsers.py
+++ b/pandas/io/parsers.py
@@ -1465,7 +1465,7 @@ def _extract_multi_indexer_columns(
 
         # clean the index_names
         index_names = header.pop(-1)
-        index_names, names, index_col = _clean_index_names(
+        index_names, _, _ = _clean_index_names(
             index_names, self.index_col, self.unnamed_cols
         )
 
@@ -3464,6 +3464,11 @@ def _clean_index_names(columns, index_col, unnamed_cols):
 
     columns = list(columns)
 
+    # In case of no rows and multiindex columns we have to set index_names to
+    # list of Nones GH#38292
+    if not columns:
+        return [None] * len(index_col), columns, index_col
+
     cp_cols = list(columns)
     index_names = []
 
diff --git a/pandas/tests/io/parser/test_index_col.py b/pandas/tests/io/parser/test_index_col.py
index f3191d5195308..a409751e261d6 100644
--- a/pandas/tests/io/parser/test_index_col.py
+++ b/pandas/tests/io/parser/test_index_col.py
@@ -226,3 +226,56 @@ def test_index_col_large_csv(all_parsers):
         result = parser.read_csv(path, index_col=[0])
 
     tm.assert_frame_equal(result, df.set_index("a"))
+
+
+def test_index_col_multiindex_columns_no_data(all_parsers):
+    # GH#38292
+    parser = all_parsers
+    result = parser.read_csv(
+        StringIO("a0,a1,a2\nb0,b1,b2\n"), header=[0, 1], index_col=0
+    )
+    expected = DataFrame(
+        [],
+        columns=MultiIndex.from_arrays(
+            [["a1", "a2"], ["b1", "b2"]], names=["a0", "b0"]
+        ),
+    )
+    tm.assert_frame_equal(result, expected)
+
+
+def test_index_col_header_no_data(all_parsers):
+    # GH#38292
+    parser = all_parsers
+    result = parser.read_csv(StringIO("a0,a1,a2\n"), header=[0], index_col=0)
+    expected = DataFrame(
+        [],
+        columns=["a1", "a2"],
+        index=Index([], name="a0"),
+    )
+    tm.assert_frame_equal(result, expected)
+
+
+def test_multiindex_columns_no_data(all_parsers):
+    # GH#38292
+    parser = all_parsers
+    result = parser.read_csv(StringIO("a0,a1,a2\nb0,b1,b2\n"), header=[0, 1])
+    expected = DataFrame(
+        [], columns=MultiIndex.from_arrays([["a0", "a1", "a2"], ["b0", "b1", "b2"]])
+    )
+    tm.assert_frame_equal(result, expected)
+
+
+def test_multiindex_columns_index_col_with_data(all_parsers):
+    # GH#38292
+    parser = all_parsers
+    result = parser.read_csv(
+        StringIO("a0,a1,a2\nb0,b1,b2\ndata,data,data"), header=[0, 1], index_col=0
+    )
+    expected = DataFrame(
+        [["data", "data"]],
+        columns=MultiIndex.from_arrays(
+            [["a1", "a2"], ["b1", "b2"]], names=["a0", "b0"]
+        ),
+        index=Index(["data"]),
+    )
+    tm.assert_frame_equal(result, expected)