The 21-year-old, who missed all of last season through injury, was sidelined for several weeks after Arsenal's defeat to Tottenham in March, and has been on the bench for the Gunners' last three league games.
On Monday, Wenger confirmed the procedure, which will remove the pin inserted previously, but said the England midfielder would be set to return for Arsenal's pre-season tour of Asia.
"He will have small mild surgery after the season. At the moment Jack plays with painkillers and I use him only when it is really needed," he said.
"It is a very small, small, small one (operation), taking out a pin. It is a two to three weeks job. It will not be a problem."
The operation will rule him out of England's friendlies against the Republic of Ireland and Brazil, on May 29 and June 2 respectively - a major blow for Roy Hodgson who names his squad on Thursday.
And Wenger admitted the Arsenal playmaker will be disappointed.
"Of course (he will be disappointed), but he will go (to Brazil) next year," he added.
Wilshere is expected to be on the bench again on Tuesday when Wenger's side face FA Cup winners Wigan, a game that could see them move into fourth place should they claim all three points.
"We are on a great run, a remarkable run. We have a good spirit, a good understanding within the squad, so let's just continue to play," Wenger added.
"Wigan is a bit repeated every year, they recover always in the period where everybody says they are finished," said Wenger.
"Of course they get out in recent years every time - just - but when you play with that fire every year it can be dangerous.
"What Wigan have done as well is always discover players, you have to give them credit for that, with a small budget they find very good players and so that is sad of course if they go."