The Spaniard has not played for the Gunners since suffering a knock during his side's 6-0 Champions League victory over Ludogorets Razgrad on October 19.
A statement on the Arsenal website read: "Santi Cazorla is travelling to Sweden early next week to undergo surgery to his right ankle.
"The club's medical team and specialists have decided that surgery is required to the plantaris tendon in the Spain international's right foot.
"We expect Santi's full recovery to take approximately three months. Everyone at the club will be working hard with Santi to make sure he's back on the pitch as soon as possible."
Cazorla has made 11 appearances for Arsenal this season in all competitions.