It was in the fourth ODI, Kumar sustained the injury when he tried to stop a David Warner shot off his own bowling which led to a fractured thumb.
Kumar, who was originally drafted into the squad in the place of injured Mohammad Shami, had a disappointing series after failing to pick a single wicket in his two appearances.
His replacement Dhawan will continue to stay in Australia after being part of the One-Day International series where he picked just one wicket in three games.
The first T20I between Australia and India is scheduled to begin on 26th January in Adelaide.
© Cricket World 2016