Kohli (847 points) has had an ordinary Test series against Australia, scoring 0, 13, 12 and 15 in the two matches so far.
New Zealand skipper Kane Williamson gained two places to reach second spot in the ICC Player Rankings for Test Batsmen.
The latest rankings, which took into account performances in the first Test between Sri Lanka and Bangladesh in Galle which the home side won by 259 runs, saw Williamson leapfrog Joe Root and Kohli after his fine knock of 130.
Williamson, who was number-one ranked for a brief while in November-December 2015, is now on 869 points, 21 points ahead of third-placed Root (848) but a good 67 points adrift of table leader Steve Smith of Australia, who's on 936 points.
Another Indian Cheteshwar Pujara is unchanged on sixth.
The top 10 of the ICC Player Rankings for Test Bowlers remained unchanged with Ashwin and Ravindra jadeja occupying first and second spots respectively after the duo spun India to a sensational victory over Australia in the second Test in Bangalore by claiming eight and seven wickets respectively.
Meanwhile, Ashwin also dethroned Bangladesh's Shakib Al Hasan from the top spot for all-rounders. Ashwin is now on 434 points, 31 ahead of Shakib (403).