The centre-back went under the knife in London on Saturday evening only hours after sustaining the setback during the first half against Arsene Wenger's side.
He faces several months of recuperation and rehabilitation.
Sources close to Villa indicate it will be "around six to seven months" before Davies fully recovers from the setback which means it could be October before he can contemplate playing again.
Davies the club's official website: "The operation went ahead on Saturday evening and the surgeon said it went very well. Obviously there's a little bit of soreness there now and I'll just have to rest it up and let everything settle down."