The England international was withdrawn from the 3-1 defeat to Aston Villa on Saturday after coming off worst in a collision with Villa defender Antonio Luna.
Oxlade-Chamberlain left the Emirates Stadium on crutches, sparking fears that he could be set for a lengthy spell on the sidelines.
However, Wenger - speaking ahead of Arsenal's UEFA Champions League play-off clash with Fenerbahce - revealed that the 20-year-old will not need an operation and could be back in action by October.
"He has a posterior cruciate problem, a ligament which is stretched," Wenger said.
"He will be out for at least six weeks. We don't think he will need surgery."
"Less than two weeks is a long time," he added "And 75 per cent of things happen in the last two days."
Arsenal have signed just one player during the close-season, bringing in Yaya Sanogo on a free transfer.
