The 23-year-old has been photographed smoking cigarettes on two previous occasions, outside a nightclub in 2013 and at a Las Vegas pool party following England's exit from the World Cup last summer.
Wenger has already publicly criticised Wilshere for smoking and the Arsenal boss will now be facing further questions about the player's off-pitch behaviour after a picture of the England international holding a pipe, reportedly taken at the weekend, was posted to Instagram and circulated on Twitter.
Wilshere is recovering from surgery on an ankle injury sustained in the game against Manchester United in November and is scheduled to make a return to the first team in the coming weeks.
His team-mate, Wojciech Szczesny, was fined €25,000 in January after smoking in the Southampton changing rooms following defeat at St Mary's on New Year's Day, and has not featured in the Premier League since.
Last summer, Wilshere vowed to learn from his "mistake" after accepting that his actions were "unacceptable": "The smoking? Of course I regret it,” he said back in July. “I’ve been seen before doing it. I said then I made a mistake and I have made a mistake again. People make mistakes.
“I’m young and I’ll learn from it. I realise the consequences it has and the effect on kids growing up. I have kids myself and I don’t want them growing up to think their dad smokes and it’s OK for a footballer to smoke because it’s not.
“It’s unacceptable and I will accept the consequences and I will move on.”
