The 28-year-old centre had become an integral part of the Wasps backline, playing in 10 of the club's 12 games since joining from Sale.
However Bell joins Tom Rees and Steve Thompson on the Adams Park sidelines after he suffered the injury in the Amlin Challenge Cup victory over Rovigo.
Director of rugby Dai Young said: "We are all gutted for Chris who has been one of our standout players all season. He has made a big impact on the field and it's a big blow for us that he won't play a further part for this length of time.
"Belly is a big part of our plans here and he will receive excellent support throughout his rehab to make sure he comes back strongly."
Rees is still some way off a return as he continues his rehabilitation from a torn ACL, while Thompson's playing career has been put on hold due to pain in his neck.
Thompson, who was forced to retire previously with a neck injury before he resumed playing again for Brive in France, now requires medical advice on the extent of the problem.
James Cannon, Joe Launchbury, Billy Vunipola and Jonathan Poff are also in the treatment room at Wasps.
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