diff --git a/doc/source/whatsnew/v1.4.3.rst b/doc/source/whatsnew/v1.4.3.rst
index bf414ab77cf65..f0e208a117068 100644
--- a/doc/source/whatsnew/v1.4.3.rst
+++ b/doc/source/whatsnew/v1.4.3.rst
@@ -19,6 +19,7 @@ Fixed regressions
 - Fixed regression in :func:`read_fwf` raising ``ValueError`` when ``widths`` was specified with ``usecols`` (:issue:`46580`)
 - Fixed regression in :meth:`.Groupby.transform` and :meth:`.Groupby.agg` failing with ``engine="numba"`` when the index was a :class:`MultiIndex` (:issue:`46867`)
 - Fixed regression is :meth:`.Styler.to_latex` and :meth:`.Styler.to_html` where ``buf`` failed in combination with ``encoding`` (:issue:`47053`)
+- Fixed regression in :func:`read_csv` with ``index_col=False`` identifying first row as index names when ``header=None`` (:issue:`46955`)
 - Fixed regression in :meth:`.DataFrameGroupBy.agg` when used with list-likes or dict-likes and ``axis=1`` that would give incorrect results; now raises ``NotImplementedError`` (:issue:`46995`)
 - Fixed regression in :meth:`DataFrame.resample` and :meth:`DataFrame.rolling` when used with list-likes or dict-likes and ``axis=1`` that would raise an unintuitive error message; now raises ``NotImplementedError`` (:issue:`46904`)
 
diff --git a/pandas/io/parsers/python_parser.py b/pandas/io/parsers/python_parser.py
index 9d68df8191338..37b2ce4c4148b 100644
--- a/pandas/io/parsers/python_parser.py
+++ b/pandas/io/parsers/python_parser.py
@@ -933,7 +933,7 @@ def _get_index_name(
                 implicit_first_cols = len(line) - self.num_original_columns
 
             # Case 0
-            if next_line is not None:
+            if next_line is not None and self.header is not None:
                 if len(next_line) == len(line) + self.num_original_columns:
                     # column and index names on diff rows
                     self.index_col = list(range(len(line)))
diff --git a/pandas/tests/io/parser/test_python_parser_only.py b/pandas/tests/io/parser/test_python_parser_only.py
index f72d22c9e5b0c..abe6c831dd4e4 100644
--- a/pandas/tests/io/parser/test_python_parser_only.py
+++ b/pandas/tests/io/parser/test_python_parser_only.py
@@ -457,3 +457,15 @@ def test_on_bad_lines_index_col_inferred(python_parser_only):
     result = parser.read_csv(bad_sio, on_bad_lines=lambda x: ["99", "99"])
     expected = DataFrame({"a": [2, 5], "b": [3, 6]}, index=[1, 4])
     tm.assert_frame_equal(result, expected)
+
+
+def test_index_col_false_and_header_none(python_parser_only):
+    # GH#46955
+    parser = python_parser_only
+    data = """
+0.5,0.03
+0.1,0.2,0.3,2
+"""
+    result = parser.read_csv(StringIO(data), sep=",", header=None, index_col=False)
+    expected = DataFrame({0: [0.5, 0.1], 1: [0.03, 0.2]})
+    tm.assert_frame_equal(result, expected)