Wilshere was forced to withdraw early in the second half at the Stadium of Light with a thigh problem, as the Gunners registered a 1-0 win.
The midfielder played the full 90 minutes for his country on Wednesday and impressed as England beat Brazil 2-1 at Wembley.
Wenger was thought to be under the impression that Wilshere would not play a full match for the Three Lions and is unhappy with England coach Roy Hodgson for breaking that agreement.
"Arsene is livid. He was led to believe Wilshere would not play the full 90 minutes," The Sun quotes an Arsenal insider as saying.
"But that is exactly what happened and then he breaks down at Sunderland. Jack only returned in October after being sidelined for 18 months, so we have to be careful with him.
"Arsene feels the fact he was overused for England contributed to his injury at the Stadium of Light."
The 21-year-old's injury is not thought to be serious and Wenger revealed in his post-match press conference that he expects Wilshere to return in four to five days.