Manager Arsene Wenger said: "Mikel has had surgery which went well. I have just seen him, he is back with us at the training ground."
The Spaniard last played on 26 November in a 2-0 win over Borussia Dortmund.
Wenger added: "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."
