The 27-year-old ruptured a cruciate ligament in his knee during the 4-1 FA Cup third-round replay win over Southend in midweek and underwent surgery in London on Saturday morning.
Cole's loss will be a massive blow to under-fire Chelsea coach Luiz Felipe Scolari.
Scolari declared: "We have had some bad news about Joe Cole, who has a knee injury and will be out for some time. It is a big disappointment for Joe and a big loss to the squad. We wish him the best recovery."
Captain John Terry added: "We're all behind Coley to get fit as soon as possible. He's going to be a big miss for us and I keep on saying he's the one who really opens things up in tight moments.
"He did it again on Wednesday against Southend. What a pass he produced for Salomon Kalou's goal.
"We're all gutted for him and we know how much it means to him to be playing.
"No-one will be more hurt at missing games through injury. But one thing we all know is that he'll work just as hard off the pitch to get fit as he does on it."