Arteta has not played for the Gunners since November 26, when he suffered a problem with his calf during a 2-0 win over Borussia Dortmund in the Champions League.
The 32-year-old was expected to be out for around a month but a subsequent problem with his ankle means rehabilitation will take "approximately three months".
"Mikel has had surgery which went well
I have just seen him, he is back with us at the training ground," Arsenal manager Arsene Wenger told the official club website.
"He had a 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."
Source : PA