The Spain midfielder suffered the injury as he netted a freak goal at Sunderland on Saturday, the ball being kicked into him by Anton Ferdinand and looping 40 yards into the goal.
He now looks set to miss the showdown with Barclays Premier League leaders Chelsea on 3rd October.
The 23-year-old had just been finding his form having returned late after reaching the World Cup final in South Africa.
With Theo Walcott, Robin van Persie and Nicklas Bendtner all still sidelined, the loss of another key man has come as a blow for the Gunners.
Fabregas would not have been included in the squad for Tuesday's match at Tottenham Hotspur, with manager Arsene Wenger again set to use a combination of fringe and youth players in the Carling Cup.
He will certainly miss Saturday's home Barclays Premier League encounter with West Bromwich Albion and the Champions League trip to Partizan Belgrade three days later.
