The 22-year-old ace had been struggling with a hamstring injury for a month now and he had hoped to be fit to play in the play-off games next month, but he aggravated the problem in training.
The Republic face either Iran or the United Arab Emirates on 10 and 15 November and Duff was determined to play in the games.
Duff had hoped to prove his fitness by making a return to the Rovers side for this weekend's game at Southampton, but he has admitted defeat revealing he needs more time to recover.
Republic boss Mick McCarthy admitted it was big blow to lose Duff, who has been so impressive of late for Ireland in their qualifiers.
"Damien needs to rest for 10 days," said McCarthy. "He told me he had no chance of making the play-offs.
"It is a huge disappointment because Damien has been on fire for us recently and would have been a great asset in the play-offs."
McCarthy is still sweating on the fitness of captain Roy Keane who is struggling with a knee injury.
The Manchester United ace has been out for the last two weeks with the problem and he is a serious doubt for the play-off games, but Sunderland winger Kevin Kilbane had declared himself fit to play.
