Wallaby Pocock limped off early in the first half of the Perth-based side's match against the Sharks on Saturday.
"It's disappointing to lose David as he is clearly one of the best players in his position in the world," Force coach Richard Graham said in a statement.
"We're fortunate, however, that the diagnosis means a relatively short time out of action, it certainly could have been much worse."
The injury will come as a hammer-blow to the struggling Force, who have lost both their opening games and have precious few second rowers to fill the ball-scavenger's boots.
"During the period David is unavailable we can look to the quality and depth we have in our backrow stocks with Richard Brown, Ben McCalman and Matt Hodgson giving an excellent balance to that area of the ground," Graham said.
Outside centre Mitch Inman, who dislocated his right elbow in the opening minutes against the Sharks, would also be out for a similar period, Graham said.
The Force were also waiting on sanction for replacement back Rory Sidey, who was cited by the southern hemisphere competition's disciplinary panel after he was sent off in the Sharks match for lifting Odwa Ndungane in a tackle.
