The 22-year-old faces at least six weeks of rehabilitation, and a further two before being up to full match fitness, after tests showed he had sustained a hairline fracture in his left foot.
The damage followed a hefty tackle from Liverpool defender Daniel Agger early in England's friendly against Denmark at Wembley on Wednesday.
Wilshere played on following treatment until he was replaced on the hour, and when speaking to reporters afterwards maintained it was "just a bruise" having been initially assessed by the Football Association medical staff at the stadium.
Arsenal confirmed the full diagnosis following consultations with an independent radiologist.
Should all go to plan, then Wilshere could be back in time for the final two Barclays Premier League matches - and possibly an FA Cup final date if the Gunners progress, with Saturday's quarter-final tie against Everton their next fixture.
England manager Roy Hodgson, who is set to name a provisional 30-man World Cup squad on May 13 - has already expressed his sympathy for both player and club.
Wenger remained pragmatic today as he said: "I had no agreement (with Hodgson over Wilshere's game time), no. It is an accident on a good ankle.
"I think the tackle was strong, but I think he (Agger) wanted to go for the ball."
Wenger indicated he would probably have done the same in allowing Wilshere to continue once the midfielder - who had looked in considerable pain initially after the impact - was back on his feet.
"It is the pain of the player that gives you the indication and you trust always the player," he said.
"Sometimes you give him a few minutes when a guy has been touched like that to tell you how he feels and if there is no pain we are not at the point where you can make an instant check up (on the pitch) with X-rays to see how big the damage is.
"Most of the time, it is the indication of the player that helps you if you can go on or not."
Wilshere has endured fitness issues since first suffering an ankle problem in the build-up to the 2011/12 campaign, and spent 17 months on the sidelines which saw him miss out on the chance to play at both the European Championships as well as represent Team GB at London 2012.
Wenger, though, is confident the 22-year-old has the strength of character to recover once more.
"He's in the boot and he's gone away for a few days to get a little bit away from travelling and the disappointment and think about something else," Wenger said.
"We want to help him come back as quickly as possible and prepare for the rest of the season."
Although it will be of little comfort, Arsenal will be compensated financially for the injury and the Barclays Premier League club will not have to pay the midfielder's wages - reportedly around £100,000-per-week - while he is sidelined, with the money coming from the FA's insurers.
Wenger sees no reason why Wilshere should not go on to play for England at the World Cup finals, unlike Arsenal forward Theo Walcott, who suffered a serious knee injury in January.
"A fracture is a fracture, it is not muscular or a ligament. Once it is healed, you do not have to have any restriction in your preparation," he said.
Wenger, though, must now plan for life without Wilshere during a period which could well define Arsenal's season.
Next week the Gunners are in Germany for the second leg of the Champions League last-16 tie away against Bayern Munich, trailing 2-0, before returning to the north London derby at Tottenham on March 16.
Wenger maintains the tough schedule will not impact on his team selection for Saturday's lunchtime kick-off against Everton in the FA Cup.
He said: "It is the quarter-final. We want to qualify and to win, that is the best way for us to prepare for the other games."