The 33-year-old pulled up while fielding on the final day and left the ground to undergo scans in hospital.
Clarke also needed treatment on Tuesday on his long-term back injury after retiring hurt while batting.
"There is a chance I will never play again." he told a news conference.
"I hope that is not the case, but you have to be realistic as well."
Clarke suffered the injury in the 44th over of India's second innings at the Adelaide Oval on Saturday as he attempted to bend down to pick up the ball while fielding.
He had injections to relieve spasms in his back while batting on the first day, but returned to the crease the following day to complete a century.
