The tourists were kept on the field for the entire first day's play as India 'A', lifted by Manoj Tiwary's impressive 93, scored 369-9 in the three-day practice match at the Brabourne stadium.
The lanky Finn, regarded as a certainty for the four-Test series starting in Ahmedabad on November 15, bowled four overs within the first hour before being confined to the dressing room for the rest of the day.
Finn is expected to have a scan to determine the cause of the discomfort in his right leg, but his absence from the field cost the tourists dearly.
The bowlers wilted under the hot sun as Tiwary and Irfan Pathan (46) put on 110 for the seventh wicket to build on sparkling half-centuries from opener Abhinav Mukund and Yuvraj Singh.
Tiwary, who turns 27 next month, put himself into Test reckoning after eight one-day appearances as he and Pathan helped the hosts recover from 186-6 in the post-lunch session. Pathan's contribution in the century partnership was a well-made 46. The duo put on a stand of 110 for the seventh wicket in 168 balls, with Pathan striking five fours and two sixes, to take the team past the 300-mark.
The Bengal captain, looking well-set for a deserving century, tried to play across against England's pacer Tim Bresnan and lost his stumps. He faced 150 balls and hit 11 fours in his 202-minute knock.
Tim Bresnan bowled Tiwary and Ashok Dinda off successive balls, but Vinay Kumar hit an unbeaten 25 to boost the total.
Earlier, Mukund survived a confident shout for leg-before from James Anderson off the fourth ball of the match to hammer 16 boundaries in an aggressive 73 off 83 balls.
Yuvraj, dropped first ball at square leg by Samit Patel, hit 59 to enhance his claims for a Test comeback after being treated for germ-cell cancer between his lungs earlier this year.
The left-hander smashed seven boundaries and four sixes in front of the national selectors, who will meet on November 5 to pick the squad for Ahmedabad.
Yuvraj played the last of his 37 Tests in November last year and hit a double-century on his return to first-class cricket earlier this month.
Off-spinner Graeme Swann and Bresnan finished with three wickets each, but Patel's 20 overs of left-arm spin cost 95 runs.