The England international was withdrawn from the 3-1 defeat to Aston Villa on Saturday after coming off worst in a collision with Villa defender Antonio Luna.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."
After the disappointing defeat to Villa on the opening day of the Premier League season, Wenger reiterated that he is looking to bolster his squad following a quiet transfer window thus far.
And he believes that he has ample time to complete the signings he needs.
"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.
