Wilshere, 24, was photographed speaking to police in the early hours of Sunday morning after reportedly being rejected from a nightclub in central London.
The England midfielder will play in the club's under-21 fixture against Newcastle United on Friday and Wenger feels that the nightclub incident did not merit the media attention it received.
“I've spoken to him. It looks to be taken out of proportion a little bit,” Wenger told a press conference ahead of his side's Premier League clash with West Ham United on Saturday.
“These are matters that we like to keep internal. This is a completely private matter. I don't know really what happened.”
He added: “There was no training session the next day. He had an off day (day off). You can accept that sometimes the players go out, when they are free the next day, over the weekend.
“Overall, what is positive is that he works very, very hard. The news looks quite good. I think he will have a good test tomorrow night.”
Wilshere has not played this season after sustaining a fractured shin in pre-season.
His list of injuries is only slightly longer than his record of off-pitch incidents, but Wenger believes that it is fitness concerns, rather than disciplinary matters, that are the only barrier to a successful career.
“At the moment I believe he's a real football brain, Jack Wilshere. He loves football,” said the Frenchman.
“He's very serious, very dedicated. The only thing that could stop him from having the career he can make is injuries.
“He had the history of his injuries. It's been bad recently. But I hope he can get rid of that and make the career he deserves.”
Wenger revealed that midfielders Aaron Ramsey and Mathieu Flamini are in contention for the trip to West Ham after thigh and hamstring injuries respectively.
He also confirmed that the club are in talks over a new contract for 19-year-old Nigerian forward Alex Iwobi, who has scored two goals in his last two appearances.
“We are discussing it at the moment, to extend,” Wenger said. “He has three years left at the end of the season, but we want to keep him here for longer.”
Arsenal are currently 11 points behind league leaders Leicester City, albeit with a game in hand, but Wenger refuses to give up on the title.
“As long as mathematically it's possible, there's a strong possibility,” he said.
“We know we need nearly the perfect run - I could have cut the 'near' out. We have just to focus on our performance and hope we finish in a very strong way.” – AFP
Original source: Wenger down plays Wilshere incident