The midfielder, 26, had the operation in London on Monday after he missed West Ham's 3-1 win over Everton on Sunday.
The Hammers have confirmed that the ex-Arsenal star is determined to make a speedy recovery after he picked up a knock during training.
Speaking on the club website, head of medical Richard Collinge said: "Jack underwent successful surgery in London on Monday morning for a minor ongoing ankle issue.
"The surgeon was happy with the procedure and all went as planned.
"We envisage he will only need a relatively short of period of rest and will then start his rehabilitation.
"Jack is focused and determined to get back training and playing as soon as possible."
But the injury-prone midfielder is now set to miss games against Chelsea, Manchester United, Brighton and Tottenham.
After joining from Arsenal in July, Wilshere played full games against Liverpool, Bournemouth and Arsenal in the Premier League.
But he was hauled off the pitch against Wolves and watched from the sidelines as Manuel Pellegrini's men picked up their first points of the season.
Mark Noble, Pedro Obiang and Declan Rice played as a midfield three, but Marko Arnautovic raised concerns when he limped off the pitch with a knee injury.
West Ham are now preparing to face Chelsea on Sunday, who have won all five of their opening games.
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