Wenger thinks Wilshere can become one of the best players in the world but he is concerned the 21-year-old may be over-used because of his high talent level.
Back from a serious ankle injury this season, Wilshere is already in fine form and was the man of the match on Wednesday night when England beat Brazil 2-1 at Wembley.
However, Wenger was a little surprised that Wilshere played the whole 90 minutes and is slightly concerned about the demands placed on his player.
"I had in fact expected Jack to play only a part of the game on Wednesday," said Wenger. "But it didn't happen and, because of his quality, he will be exposed to that.
"The overuse of his quality, you can understand that. He will have to be managed like everyone else.
"It is not just the physical aspect but the mental pressure every time he plays. We will have to manage him well physically to make sure he doesn't face that burnout."
And Wenger believes there is no limit to what Wilshere can achieve in the future, as long as he stays fit.
"You do not want to set any limit on the development of any player, especially when he plays at that level at his age," said Wenger.
"The most important thing for me will be to keep his passion for the game, and keep his attitude of wanting to become a better player.
"If he keeps these two ingredients that are not always easy, he can of course become a fantastic player. He is already one, but he can become one of the best in the world, yes.
"Let's not forget that he is only 21 now, and he starts his career really, because he was out for 17 months. The influence he has today on the England team already is absolutely fantastic."