The 22-year-old England international had to be operated on after he damaged ankle ligaments in a challenge with Paddy McNair during Arsenal's 2-1 loss at home to Manchester United last weekend.
"Jack Wilshere has had successful surgery on his left ankle and will be out for approximately three months," Arsenal said in a statement on the club website.
"An assessment with a specialist confirmed the need for an operation and the 22-year-old had successful surgery to his ankle in London on Thursday afternoon."
Wilshere missed the entirety of the 2011-12 season with a stress fracture of the ankle, but on that occasion the injury concerned his right ankle.
His latest lay-off, which could last until early March, exacerbates the injury problems currently facing Arsenal manager Arsene Wenger.
Right-back Mathieu Debuchy and playmaker Mesut Ozil are long-term injury victims, while goalkeeper Wojciech Szczesny, midfielder Mikel Arteta and striker Danny Welbeck have each developed problems over the past week.
Szczesny injured his hip against United, while Arteta was forced off during Arsenal's 2-0 win at home to Borussia Dortmund in the Champions League on Wednesday with a calf injury that Wenger said looked "quite serious".
Welbeck sat out the Dortmund game after complaining of tightness in his hamstring.
Striker Olivier Giroud and centre-back Laurent Koscielny are both fit after spells on the sidelines, but winger Theo Walcott's return from a serious knee problem has been delayed by a groin injury.
Source : AFP
Source: AFP