Wilshere has not featured for the Gunners in a competitive game this season after suffering the injury in a pre-season friendly against the New York Red Bulls at the Emirates Stadium.
A statement on the club's official website on Monday evening read: "Jack Wilshere has on Monday morning undergone ankle surgery at a central London hospital.
"Under the care of two world-renowned surgeons, Jack has had the stress fracture of his right ankle repaired.
"The initial indications are that the surgery has been successful and Jack will now undergo a prolonged period of rehabilitation. It is envisaged that Jack's rehabilitation will take a period of four to five months."