Wilshere struggled to get on the pitch for Arsenal in the second half of last season due to injuries, continuing on from an injury-interrupted 2012/13 Premier League campaign, prompting Graham to claim the 22-year-old midfielder's career has "not gone anywhere in the last 18 months".
Although Wilshere was part of England's squad at the FIFA World Cup, he has been in the media for all the wrong reasons this week after photos emerged of him smoking while holidaying in Las Vegas, just nine months after vowing to give up cigarettes.
Graham said Wenger - as Arsenal's manager - must get Wilshere to change his behaviour or risk seeing the talented Englishman fail to fulfil his potential.
"After the bad publicity shots in the newspapers, somebody has got to have a word with him and I think Arsene Wenger will do," Graham told talkSPORT on Tuesday.
"His [Wilshere's] career has not gone anywhere in the last 18 months. The papers now want any sort of publicity of players misbehaving and he has got to get his act together.
"Arsene Wenger has to have a word with Jack and tell him the responsibility he has now got. They were talking about him being a future Arsenal captain and a captain shouldn't be acting like that."
Meanwhile, former Arsenal defender Ashley Cole claimed smoking does not always affect footballers' ability to perform on the pitch, although he conceded Wilshere's public image will suffer if he does not stop.
Wilshere was photographed smoking in October last year but said afterwards he is not a smoker and vowed never to smoke again.
"Everyone talks about footballers having to be professional and be an example but we don't know if the smoking affects him [Wilshere]," Cole said.
"Of course I am not condoning smoking. We don't want smoking. I have smoked before, I have stopped.
"It didn't really affect me the way I run but of course it's not a good thing to do in public. But he is a young lad and he will learn."
