A picture of Wilshere holding the pipe at a London nightclub has been circulated on social media over the past few days, and is the third time the midfielder has been photographed in such a way.
He was first snapped emerging from another nightclub with a cigarette in his hand in 2013, and again last summer while at a Las Vegas pool party following England's World Cup exit.
Wenger has taken a dim view of the 23-year-old's latest indiscretion and is set to keep any disciplinary action behind closed doors, as he did so after Wojciech Szczesny was caught smoking in the Southampton changing rooms on New Year's Day.
The Gunners boss has denied that there is a culture of smoking at his club, though, and has publically played down the latest storm surrounding Wilshere.
"There is no smoking culture at Arsenal," he said.
"I talked to Jack. He is sorry for what happened. He is not a smoker. He had a day off the next day. It is down to him to master his life.
"You've been 20 as well, you need to relieve pressure. One photo, a second of your life doesn't tell the story of your life. I had some photos in Brazil and didn't even know the people around me."
Wilshere was first snapped emerging from another nightclub with a cigarette in his hand in 2013, and again last summer while at a Las Vegas pool party following England's World Cup exit.
