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

Rohit batted at number nine with stitches in the hand and hit a valiant 51 not out in his team's five-run loss to Bangladesh, who took an unassailable 2-0 lead in the three-match series, in Dhaka.

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.

"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 for scans after he took a hit while attempting a catch at slip in Bangladesh's innings.

Rohit dropped Bangladesh opener Anamul Haque in the second over of the match as the ball seemed to caught his webbing between the thumb and first finger with blood oozing out as he walked off the field.

Dravid hailed Rohit's courage to run Bangladesh close with an injured hand after India had slipped to 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.