Wilshere sustained a hairline fracture to the navicular bone in his left foot following a challenge with Daniel Agger in England's friendly win over Denmark at Wembley on Wednesday that will rule him out for up to six weeks.
The injury casts a major doubt on the midfielder's inclusion in Roy Hodgson's provisional 30-man England squad for the FIFA World Cup finals, which is due to be named on May 13, and means he will miss a number of key fixtures for Arsenal.
Amid reports that Arsenal could seek financial damages from the Football Association as a result of the injury, Wenger insisted he was largely concerned at losing a player of the 22-year-old's calibre.
"Our shock was losing a competitive player, the finance is not my main worry at the moment," he said on Friday.
"The tackle was strong but I think he wanted to go for the ball.
"You want to encourage him to go to the World Cup and I will do absolutely everything to help him get there.
"When you are Jack's age you just want to play. Certainly his injuries have a weight on his mind."
Ahead of Saturday's FA Cup quarter-final with Everton, Wenger is adamant Arsenal are in a strong position to challenge for a first trophy since 2005.
"What is different this year is that we are in a better position to win trophies. We are ready for the battle," he added.
"It is one of the priorities, it's very important to come back with a strong response."
Wenger's only other injury concern for Saturday is Laurent Koscielny, who was described as a "doubt" by the Arsenal boss.
Midfielder Aaron Ramsey is set to return to action for the north London derby against Tottenham next weekend, while January acquisition Kim Kallstrom could make his debut at White Hart Lane after overcoming a back problem.
