Finn, who was injured during England's first warm-up match of the tour, was expected to be recalled for the second Test here to bolster the English attack which failed to make an impression in the first Test in Ahmedabad.
He is now, however, expected to undergo a scan tomorrow to know the extent of the problem.
England are certain to make changes to their bowling attack for the second match with left-arm spinner Monty Panesar likely to come back.
The batting line-up could also be slightly altered as Ian Bell has flown home for the birth of his child.
Skipper Alastair Cook, after the failure in the first Test, urged all his players to chip in.
Cook made a defiant 176 in the second innings but could not avert a nine-wicket defeat.