Wilshere, who has struggled with injuries in recent seasons, went out with friends and team-mates on Wednesday night, 24 hours after the 2-0 Champions League victory over Napoli.
The Sun published a photo of the England international appearing to take a drag on a cigarette outside posh West End nightclub Dstrkt, leading Wenger to publicly warn the 21-year-old about his conduct.
"Well, I disagree completely with that behaviour," Wenger said at Arsenal’s pre-weekend press conference. "I need to have a chat with him about that. (What I say) I will leave between him and me.
"When you're a football player you're an example, and you don't do what damages your health.
"You can damage your health at home - you can smoke or drink at home - and nobody sees it, but when you're out socially, you damage your reputation as well."
Wenger added that attitudes to smoking may be different on the continent, but that he feels Britain's relative aversion to tobacco is correct.
"I've travelled as a football player on coaches after games in France where you didn't see each other - there was so much smoke on the coach, everybody smoked," he added.
"But times have changed. English society is very sensitive to smoking... so it's a bit more shocking here than it is somewhere else."
Wilshere spent a total of 17 months out with an ankle injury and associated fitness problems, and in the earlier stages of his career was involved in two alcohol-related incidents.
While he has since kept his nose clean, this latest controversy suggests he is not taking his health as seriously as he should.
The player’s spokesman, meanwhile, insisted that the player does not smoke and that he was dared to hold the cigarette by a friend.
"A friend dared Jack, who does not smoke, to momentarily hold the cigarette as part of a prank. Jack absolutely didn't smoke the cigarette and nor does he condone smoking.
"Jack is utterly committed to fitness and a healthy lifestyle. In no way is this picture an accurate reflection of his attitude to smoking."
Wilshere later took to Twitter, sharing a photo of the legendary Zinedine Zidane puffing on a cigarette, before insisting he does not smoke.
Arsenal, who are top of the Premier League after six matches, visit West Brom on Sunday.