India skipper Rohit Sharma was set to fly back home Thursday to seek medical advice for a thumb injury and will miss the final one-day international against Bangladesh, coach Rahul Dravid said.

Rohit heroically batted at number nine with stitches and a bandage on his left thumb to hit a valiant 51 not out in his team's nailbiting five-run loss to Bangladesh.

The victory in front of an ecstatic home crowd in Dhaka gave the hosts an unassailable 2-0 lead in the three-match series.

The captain adds to India's growing injury list with Kuldeep Sen, who missed the match due to stiffness in his back, and fellow quick Deepak Chahar, who bowled just three overs due to a hamstring strain, also ruled out of the series.

"(We are) struggling with a few injuries, which is not ideal, not easy for us," Dravid told reporters after the loss.

"Kuldeep and Deepak are out of the series. Rohit will miss the next game, fly back to Mumbai consult with an expert and see how it is and whether he could come back for the Test matches or not, I am not sure. Too early to say."

India and Bangladesh will play two Tests starting December 14.

Rohit, who hit five sixes in his blitz and needed a six to win on the final ball when Mustafizur Rahman held his nerve, had gone off the field early in Bangladesh's innings.

He dropped Bangladesh opener Anamul Haque in the second over at slip as the ball seemed to catch the webbing between the thumb and forefinger with blood oozing out.

Dravid hailed Rohit's courage to run Bangladesh close with an injured hand after India had slipped to a hopeless-looking 207-7 in their chase of 272.

"It was phenomenal for him to show that level of courage. He had a serious dislocation, had to go to hospital to get that set right, stitches in his hand, couple of injections to just go out and bat," said Dravid.

"Credit to him, to go out and take a chance and amazing how close he got us with that innings."

Dravid said the team should have a fully fit squad come January as they will look to "address" issues in the year of the 50-over World Cup.

Rohit said that India's growing injury list was perhaps because of the gruelling workload.

"Maybe they're playing too much cricket. It's something we have to sit down with our team... and try and monitor their workload," he said.

"(We) can't afford to have half-fit players representing India," he added.