The French boss has had his position at the club questioned in recent days following his side's slow start the to the new Premier League season.
However, England international Wilshere has backed Wenger to turn things around at the Emirates Stadium soon.
"He has been there for 15 years and been great for Arsenal," the 19-year-old told the London Evening Stadium. "The criticism Arsene gets is just a joke.
"We do get a harder time from the critics than most teams but we haven't won anything for six years and that's not good enough for Arsenal.
"It is harsh, though, especially on the boss. We started a bit slowly but we still feel we can finish in the top four."
Wilshere is currently recovering from an ankle injury that could keep him sidelined until the New Year.