The Borat actor stars alongside Hugh Jackman, Anne Hathaway, Russell Crowe and Amanda Seyfried in the big screen adaptation of the Broadway musical.
Cohen plays thief Monsieur Thenardier in the film, which is being helmed by The King's Speech director Tom Hooper.
According to The Sun, shooting on the movie has been pushed back to give the 40-year-old time to rest his vocal cords.
Hooper has made the choice to have all actors in the film sing their musical numbers live, which has apparently taken a toll on Cohen's voice.
A source involved with the productions said: "Sacha is taking some time out. It's a real shame because the new shooting dates have resulted in some singers becoming unavailable as they have prior engagements which have to be fulfilled first."
Les Misérables opens in cinemas on December 14 in the US and January 11 in the UK.
Watch a trailer for Les Misérables below: