Rahul will now return home to begin his rehabilitation process at the NCA.
In a media release, the BCCI on Tuesday (January 5) said that the 28-year-old sprained his left wrist while batting during a practice session at the Melbourne Cricket Ground (MCG) last Saturday.
"KL Rahul sprained his left wrist while batting in the nets at the MCG during Team India’s practice session on Saturday. The wicketkeeper-batsman will not be available for the remaining two Tests of the Border-Gavaskar Trophy as he will need about three weeks time to recover completely and regain full strength," BCCI said in a statement.
“He will now return to India and head to the National Cricket Academy in Bengaluru for further rehabilitation of his injury,” it added.
The visitors are already missing the services of skipper Virat Kohli, who is on paternity leave, Mohammad Shami and Umesh Yadav – due to injuries.
Rahul was not part of the playing XI for the first two Tests but featured in the white-ball leg of the Australia tour.
India had won the Boxing Day Test by 8 wickets to level the series at 1-1. The third Test will be played at the Sydney Cricket Ground from January 7.