The stage adaptation of Iain Softley’s 1994 film, which opened in London in October, had been booking until 24 March.
Following its London outing, producers are hoping to transfer the show to Canada in the summer of 2012.
Speaking about the production, producer Karl Sydow said: “I am enormously proud to have brought Backbeat to London and look forward to working with David Mirvish to take this great production to Canada next year.”
Backbeat follows the fortunes of the world’s most famous band as they leave Liverpool behind to play rock ‘n’ roll cover versions on the Reeperbahn. As, night after night, they play tracks including Mr Postman and Twist And Shout, Backbeat explores the love triangle between John Lennon, original bassist Stuart Sutcliffe and German photographer Astrid Kirchherr.
News of Backbeat’s closure swiftly follows the announcement that Scrubs star Zack Braff will make his West End debut in his own play, All New People, which will begin a London run at the Duke of York’s theatre on 22 February 2012.