He has a hairline fracture of the left leg and has not played this season.
"Jack will have surgery in London in the forthcoming days. This will involve inserting a small plate in his left fibula," the club said on their website (www.arsenal.com). "Jack is likely to be out for approximately three months."
He will miss England's final European Championship matches next month.
Wilshere, 23, who missed the whole of the 2011-12 season through injury, managed only 14 league games last season.
It is a further blow for Arsenal, whose England striker Danny Welbeck is out for some time following knee surgery.
(Reporting by Steve Tongue, editing by Pritha Sarkar)
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