The beanpole Middlesex paceman bowled four overs before being injured while chasing a ball in the outfield and was confined to the dressing room for the rest of the day.
Scans later on Tuesday did not reveal any major damage but Finn was asked to sit out for the rest of the match to undertake a recovery programme set out by team doctors.
"Steven Finn has been ruled out of the remainder of the three-day game with a right thigh strain," team spokeswoman Rhian Evans said.
"He will be assessed over the next couple of days to determine a rehabilitation programme."
England are not calling in a replacement, but Finn may be required to play at least one of the two remaining warm-up matches to be considered for the Ahmedabad Test.
The tourists take on Mumbai 'A' in a three-day game from Saturday and play state side Haryana in a four-day match in Ahmedabad from November 8.
Finn has played 16 Tests since his debut against Bangladesh in 2010, claiming 66 wickets at an average of 28.15. He has taken five wickets in an innings three times.