"Steve Finn has been ruled out of remainder of the three-day game with right thigh strain. He will be assessed over the next couple of days to determine a rehabilitation programme," said a spokesperson of the England and Wales Cricket Board travelling with the team.
The 23-year-old Finn, from English county Middlesex, is yet to play against India in Tests and has taken 66 wickets from 16 Tests.
The lanky fast bowler bowled only four overs for 22 runs without taking a wicket in the opening session of play on day one yesterday at the Brabourne Stadium and took no further part as India A raked up 369 for 9 by close in 90 overs.
The touring side will next take on Mumbai A in their second three-day game at the D Y Patil Stadium in Navi Mumbai.
England play a four-day game on Ground A of the Motera Stadium in Ahmedabad from November 8-11 before the first Test against India commencing in the main ground there on November 15.