Arsenal will also be without France international defender Mathieu Debuchy until April following surgery on the shoulder he injured against Stoke City last weekend.
Spanish midfielder Arteta had a bony spur removed and in a statement on their website, Arsenal said: "The procedure went well and Mikel will now begin a period of rehabilitation which is expected to last approximately three months."
Manager Arsene Wenger added: "Mikel has had surgery which went well.
"He had limited mobility in his ankle and some persistent inflammation that had an impact on his calf.
"That meant we had to make the decision to have surgery and it's a proper solution which gives him the best chance to recover."
He has not played since being substituted in the 67th minute of Arsenal's 2-0 win over Borussia Dortmund in the Champions League at the Emirates Stadium on November 26.
Wenger added that 29-year-old Debuchy had surgery on his right shoulder following his injury.
"It's very unfortunate for Mathieu, it's unbelievable because he's had two surgeries in the same season.
"He just came back, he played seven games and he's out again. I count three months out for Mathieu because contact will be a problem for the shoulder."
Debuchy started Arsenal's first seven matches of the season including the Community Shield win over Manchester City at Wembley and then missed the next three months after damaging his ankle against City on September 13.
He returned to the side for the Champions League match against Galatasaray on December 9 and retained his place in the starting line-up before his latest setback which came after a collision with Stoke's Marko Arnautovic sent him crashing into the advertising boards.
