Rizwan and Irfan both suffered hamstring injuries in the third match in Rawalpindi, where a second-string New Zealand side won by seven wickets to level the five-match series 1-1
Kohli, who hurt his shoulder while diving to stop a boundary in the drawn third test in Ranchi, was hoping to be fit for the decider at the Himachal Pradesh Cricket Association Stadium which is hosting its first test.
Ajinkya Rahane will lead India in Kohli's absence, Bangar told the host broadcaster.
The four-match series between the world's top two test team is level at 1-1.