The 20-year-old was left out of the Arsenal squad that claimed a 3-2 win in the FA Cup final against Hull City this weekend.
Wenger has admitted that Oxlade-Chamberlain could have played some part in the match at Wembley, but he lacked the required fitness levels needed for the occasion.
"He was desperate to play in the cup final," The Mirror quotes Wenger as saying. "Pain-wise he could have played. I judged him short physically. I felt that in this game we wanted to play players who were completely fit and prepared. He was a bit short physically.
"The medics said to me he could play 20 or 30 minutes but you can't programme it like that. That's why I left him out. He's on the way up but he needs more fitness work now."
"But he's okay for England, yes. It was hard to leave him out. Alex and Jack Wilshere will both go to Portugal."
Oxlade-Chamberlain has made 14 appearances for the England national side, scoring three goals.