Oxlade-Chamberlain has a groin injury, and Wenger said earlier this week he was giving the Arsenal midfielder "a complete rest for two weeks".
Roy Hodgson has spoken to Wenger and does not believe the problem will affect the player's World Cup chances.
But the England manager plans to name a provisional squad on May 12, and Oxlade-Chamberlain appears increasingly unlikely to play before then.
Wenger told the club website: "Alex is in treatment at the moment and not in training. It is very difficult to give you a timescale on him at the moment."
Hodgson said on Tuesday: "From my conversation with Arsene, I don't think there is too much to worry about with Oxlade-Chamberlain."
Hodgson also expects Jack Wilshere to be fit for Brazil, although the midfielder will not feature for Arsenal against West Brom this weekend.