"He will be out for six to eight weeks but he won't need surgery," Wenger told reporters ahead of Arsenal's clash with 16th-placed Swansea City on Wednesday.
"We feared he would when we saw the MRI scan but in the end it is positive news."
A mid-April return would give Oxlade-Chamberlain time to prove his fitness ahead of the June 10-July 10 Euros where England have been drawn in Group B alongside Russia, Wales and Slovakia.
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The 22-year-old missed Arsenal's 3-2 loss at Manchester United on Sunday which left the Londoners five points behind surprise leaders Leicester City with 11 games to play.
Arsenal were heavily criticised by pundits after the defeat, but Wenger said his side could bounce back and land a first league title since 2004.
"We want to transform negatives into positives to create more solidarity. We play to fight for the title," he said.
"We gave a lot against Barcelona and that certainly had an impact on our belief against Manchester United. We're not happy with the result. We had two lapses of focus that we paid for."
(Reporting by Simon Jennings in Bengaluru. Editing by Patrick Johnston)
