The 20-year-old, who has become a key part of Roy Hodgson's national squad, limped out of Arsenal's 3-1 home defeat by Aston Villa on the opening day of the new Premier League season.
Reports have suggested he could be set for a lengthy spell of rehabilitation, however Wenger moved to calms fears of a serious injury as he spoke ahead of the Champions League play-off first leg against Fenerbahce.
"He will be out for at least six weeks, he has a posterior cruciate problem, a ligament which is stretched," said the Arsenal manager.
"We don't think it will need surgery, he is consulting tonight (Tuesday), but it will be at least six weeks out."
Oxlade-Chamberlain, therefore, can expect to miss September's crunch Group H World Cup qualifiers against Moldova and Ukraine.
The midfielder, though, could have an outside chance to recover in time for the October dates against Montenegro and then Poland as the Three Lions bid to reach next summer's finals in Brazil.