Wilshere was criticised by Wenger last season after he was seen smoking a cigarette outside a nightclub and the England international responded by insisting it would not happen again.
Yet the 22-year-old was photographed smoking this week during a swimming pool party while on holiday with members of his family.
Wenger wants to find out what exactly happened and plans to speak to Wilshere shortly.
Speaking after Arsenal’s 2-0 friendly win at Boreham Wood on Saturday, he told his club’s official website: “I know what you can make of pictures – I have to speak to him really to see what happened before I come out publicly.
“I’m not deeply concerned by it. I just want to know what happened and before I know what happened, I don’t want to talk too much about it.”
A common consensus is that Wilshere’s career has stalled over recent years, with injury and loss of form costing him his place in both the Arsenal and England teams last season.
And Wenger insists the coming campaign will be an important one for the talented midfielder if he is to fulfil his potential.
“He’s at an age where you want him to move forward,” Wenger said.
“He has the potential. I believe for him, the most important (thing) now is to have a good preparation and focus on getting really fit.
“Jack is a great player – he has a football brain and he’s ambitious. I’m sure that if he’s injury free, he will have a great season.”
Wenger has signed France defender Mathieu Debuchy and Chile winger Alexis Sanchez already this pre-season and he claimed more new faces will arrive.
Spain midfielder Cesc Fabregas opted to go to Chelsea rather than return to Arsenal, prompting delighted taunts from Blues boss Jose Mourinho, but Wenger says he won’t lose any sleep over his rival’s jibes.
“I think people came out and said he wanted to go to Chelsea. I don’t know who tells the truth here or not. He landed where he wanted to go,” Wenger added.