Bangladesh beat India by five runs in their second one-day international in Mirpur, sealing a 2-0 series victory with one game left to play.
Sharma (51 not out) came in to bat at number nine after undergoing a scan for a left thumb injury he sustained when he dropped Anamul Haque in the second over of Bangladesh's innings, and he rode his luck to take India close.
Deepak Chahar and Kuldeep Sen are also out of the series, India's head coach Rahul Dravid told reporters.
"Kuldeep and Deepak are out of the series, Rohit as well will certainly miss the next game, fly back to Bombay, consult with an expert and see how it is and whether he can come back for the Test matches or not," Dravid said.
"All three of them won't play the next game for sure," he added.
India and Bangladesh meet in the final game in Chattogram on Saturday before playing two test matches.
Check out the ful scorecard from the second ODI with Flashscore.
