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Gunners manager Arsene Wenger rated the influential midfielder's chance to be fit for the match as 50-50 but confirmed that he will miss the trip to Stamford Bridge on Sunday.
"Fabregas is not fit to play in this one and nor is (Manuel) Almunia," the French tactician said.
Lukasz Fabianski is set to stand between the sticks till Almunia reaches full recovery.
Arsenal will also have to do without left-back Kieron Gibbs, who picked up a calf problem in Tuesday's win over Partizan Belgrade in the UEFA Champions League.
"We lost Gibbs as well on Tuesday night with a calf problem and he is out of the England squad as well. He is out for two to three weeks," Wenger added.