The Spain midfielder suffered a hamstring 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.
But he told his official Twitter account: "Good news on my injury.
"I have some fluid but nothing bad in the muscle. I hope I can be playing in two weeks."
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 for a lengthy period would have come as a blow for the Gunners.
Fabregas would not have been included in the squad for Tuesday's game at Tottenham, with manager Arsene Wenger again set to use a combination of fringe and youth players in the Carling Cup.
He is likely to miss Saturday's home Premier League encounter with West Brom and the Champions League trip to Partizan Belgrade three days later, but could be back in contention for the trip to Chelsea on October 3.