Clarke, who has a history of back issues, was on 60 when he called for the trainer after twisting while at the crease.
He trudged disconsolately from the field after treatment and retired hurt, making way for Steve Smith.
A Cricket Australia spokesperson said Clarke later left the Adelaide Oval with the team doctor for further assessment on his lower back.
Clarke had to pass a fitness test on recurring hamstring problems to play in Adelaide and his departure was a big blow to the Australians, who were well on top of the Indian bowlers.
At the time of his retirement, Clarke had put on 118 runs with David Warner, who had earlier raised his 10th Test century off just 106 balls.