diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index ab9f303bec6aa..30f71201ed3dc 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -147,7 +147,7 @@ MultiIndex
 I/O
 ^^^
 
--
+- Bug in :func:`read_csv` raising ``TypeError`` when ``names`` and ``parse_dates`` is specified for ``engine="c"`` (:issue:`33699`)
 -
 
 Period
diff --git a/pandas/io/parsers.py b/pandas/io/parsers.py
index 5b623c360c3ef..7a56b03326762 100644
--- a/pandas/io/parsers.py
+++ b/pandas/io/parsers.py
@@ -1431,7 +1431,7 @@ def _should_parse_dates(self, i):
                 name = self.index_names[i]
             else:
                 name = None
-            j = self.index_col[i]
+            j = i if self.index_col is None else self.index_col[i]
 
             if is_scalar(self.parse_dates):
                 return (j == self.parse_dates) or (
diff --git a/pandas/tests/io/parser/test_parse_dates.py b/pandas/tests/io/parser/test_parse_dates.py
index 119b4090dd4c7..c0b29d5019675 100644
--- a/pandas/tests/io/parser/test_parse_dates.py
+++ b/pandas/tests/io/parser/test_parse_dates.py
@@ -1595,3 +1595,12 @@ def test_missing_parse_dates_column_raises(
         parser.read_csv(
             content, sep=",", names=names, usecols=usecols, parse_dates=parse_dates
         )
+
+
+def test_date_parser_and_names(all_parsers):
+    # GH#33699
+    parser = all_parsers
+    data = StringIO("""x,y\n1,2""")
+    result = parser.read_csv(data, parse_dates=["B"], names=["B"])
+    expected = DataFrame({"B": ["y", "2"]}, index=["x", "1"])
+    tm.assert_frame_equal(result, expected)