The 33-year-old, who picked up the injury during the ongoing ODIs against South Africa, might have to undergo surgery, according to media reports here.
"We are putting the World Cup and Ashes right up there and if he's right for the Indian Test series so be it," team performance chief Pat Howard told Fairfax Media.
"But we've seen him rushed back and what we'd hate is for him to play a Test or two and then break down. Everything is on the table at this point. We saw (paceman) Nathan Coulter-Nile go through hamstring surgery and come back in eight weeks, so obviously that is one possibility," he explained when asked about Clarke's availability for the series against India.
"I have talked about the priorities and what they are. Sometimes you have got to take a little bit of a long-term and a medium-term picture," Howard said.
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"If we do this well, we can get extra years out of Michael who is a world-class player, rather than thinking in days and tournaments. We have an opportunity to really get the best out of the last couple of years of his career.
Wicketkeeper Brad Haddin could be named Australia's captain if Clarke fails to recover for the series which starts December 4 in Brisbane.