Fabregas travelled to Barcelona yesterday to consult specialist doctor Ramon Cugat about the problem he picked up during Sunday's Barclays Premier League draw with Liverpool when he was tackled by Xabi Alonso.
The injury is set to keep the Gunners' captain sidelined for around four months, but it will not require the Spain international to go under the knife.
"After consulting with the best doctor possible, we've decided not to operate. If it would have been necessary it would have been the first thing I would have done, but the doctor recommended to me not to do it because I'm young and the meniscus is not damaged," Fabregas told Marca.
"Although we cannot be certain because the injury only happened a few days ago, but I will be out for more or less four months. My intention is to return as soon as possible to help my team-mates.
"I will endeavour to return as soon as possible to do what I like most, to play football."