England coach Andy Flower revealed that the Middlesex paceman faces a second scan on Wednesday to assess the injury, which he picked up on the opening day of England's first warm-up match against India A.
England will be without Ian Bell as they bid to bounce back from their first Test defeat in Ahmedabad as he has already returned home for the birth of his first child.
"Steven has been working hard to get back to full fitness," said England coach Andy Flower.
"He has unfortunately hurt his leg again a couple of days ago, and is having another scan.
"We don't think he's got any structural damage, but it would be careless to suggest that he might play the second Test."
Should the scan reveal more positive news, he could play in an England Performance Programme match ahead of the final two Tests in Kolkata and Nagpur.
"What we might do is send him off to the performance programme that arrived in India earlier this (Tuesday) morning," added Flower.
"They've got a three-day game starting on the November 27. If he's ready for that, which is the last day of the second Test, we'll put him through his paces in that.
"If he comes through that well, he'll be available for the third and fourth Tests."
England have come under fire for their nine-wicket defeat in Ahmedabad.
They were forced to follow on after replying to India's 521-8 declared with just 191, but produced a much-improved second innings of 406 to take the match to the final day.
However India lost only the wicket of Virender Sehwag as they knocked off 80 runs to seal the emphatic win.
A dedicated second spinner in the form of Monty Panesar is expected to come into the attack, with Finn's deputy Tim Bresnan likely to drop out.