Wright, who scored 185 goals in 289 games for Arsenal, spoke about how Wilshere needs to start to focus on his football:
"You just want that maturity to start to kick in because at some stage he's got to focus on being a top footballer.
"He wants to be a great footballer and leave a legacy, rather than having people talking about his off-field activities. For Jack, at some stage that has to kick in for him. And I'm sure it will."
Arsenal's diminutive midfielder has not kicked a ball all season for club or country, although he has recently been introduced back to full first-team training.
The former Crystal Palace and England striker went on to say how Wilshere must be more astute in choosing the company that he keeps:
"You just have to be a bit more mature and wiser about the company you keep. That's the only thing he has to learn, is the company you keep and the places you go."
Arsenal have seven games left in their season, and can't afford any more slip ups as they try to cut their way into Leicester City's lead at the top.
Arsène Wenger will need all of the players at his disposal to be at the peak of their powers for the run in, and Wilshere will hope that his recent actions do not affect his chances of first team game time.
However, Wright doesn't think the incident will affect his former club:
"I've been in dressing rooms where people have been caught out in respect of off-field controversies. But when you play, you play. You get on with it."
Next up for Arsenal is a trip to Upton Park on Saturday, where they face sixth placed West Ham United.