The 28-year-old, who featured in the recent ICC Champions Trophy, was injured after Monday's Friends Life t20 victory over Kent.
Batsman and former captain Mark Pettini could also be out for two to four weeks with a quad injury.
Head coach Paul Grayson said: "It's obviously very disappointing that two important players are going to be missing in all forms of the game for a while.
"Mark's effectiveness at the top of the order ensured that we got our innings off to good start and Ravi had done so well for us batting at number five while he's also an integral part of our bowling attack."
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