The midfielder has returned to training after spending the entire season so far on the treatment table.
England manager Roy Hodgson will name his 23-man squad for the European Championships on May 12, and Wenger believes that Wilshere will be fit to play if selected.
"I'll be cautious with him now but he will be back fully competitive in a few weeks," Wenger told reporters in Friday's press conference. "Yes [he can make England squad].
"Once he will be completely fit and competitive he will be available for Arsenal and the national team. Why not?"