Cohen, 40, who is set to portray thief Monsieur Thenardier in the musical drama, has to sing his numbers live for the film, reported Ace Showbiz.
"Sacha is taking some time out. It's a real shame because the new shooting dates have resulted some singers becoming unavailable as they have prior engagements which have to be fulfilled first," a source said.
The ensemble cast of the film includes Russell Crowe, Hugh Jackman, Anne Hathaway, Amanda Seyfried, Eddie Redmayne, Aaron Tveit, George Blagden and Samantha Barks.
Written by William Nicholson, the Broadway-adapted movie centres on the struggle by ex-con Valjean to outrun his past and his relentless pursuer Javert.
The movie is scheduled to be released in the US on December 7.
