Wenger: Wilshere must 'master his own life'
The picture, believed to have been taken at a London nightclub last week, was uploaded to photo-sharing website Instagram on Tuesday before being deleted and subsequently re-posted on Twitter.
England international Wilshere - who has twice been pictured smoking in the past - hit back by posting a video of himself in training on Instagram, captioned: "Worry about your character not your reputation, because your character is who you are and your reputation is only what people who don't know you think about you."
Nevertheless, Wenger revealed in his pre-match press conference prior to Saturday's north London derby with Tottenham that Wilshere - out of action with an ankle problem - had apologised for the incident.
"I have spoken with him about that," Wenger said. "He is not a smoker, he is sorry about what happened, but he has to master his own life. He had a day off the next day."
Wenger will not risk forward Alexis Sanchez against Tottenham after he missed last weekend's 5-0 win over Aston Villa with a hamstring problem, but is confident Arsenal have enough to cope without the Chile star, who has 18 goals to his name this term.
"It's not easy to tell him [Sanchez] he's not playing. He wants to play - he's so keen," Wenger added.
"But we have enough offensive power. We don't need to worry about being short on that front."
Striker Danny Welbeck is back in contention following a thigh injury that has seen him spend the last month on the sidelines.
However, newly acquired defender Gabriel Paulista will not be included despite being fully fit to play.
Wenger said: "Gabriel is physically ready to play but is not used to our back four and hasn't mastered the language yet."