The midfielder impressed during the Three Lions' victory over Brazil at Wembley on Wednesday but the French boss is concerned that the 21-year-old is doing too much too soon following his year-long layoff with injury.
"We will have to manage him well physically to make sure he doesn't have to face burnout," Wenger said in a press conference.
"I expected Jack to play only a part of the game on Wednesday night, but it didn't happen. Because of his quality, he will be exposed to that kind of issue, but will have to be managed like everyone else."
Meanwhile, Arsenal are preparing to go up against Sunderland at the Stadium of Light on Saturday.