The Englishman sustained ligament damage in the second half of his side’s first leg Round of 16 Champions League clash against Barcelona, with Wenger revealing the 22-year-old would be out for “a few weeks”.
Oxlade-Chamberlain has since undergone scans which will set him back longer than expected, yet the good news for the club is that surgery will not be required.
"We thought there could be some [surgery] when we saw the MRI but we got positive news," he told a news conference.
"The next eight weeks means March, April he will be out. He should be alright [for Euro 2016]."
Following their defeat to Manchester United, Arsenal will take on Swansea City on Wednesday before facing London rivals Tottenham Hotspur on Saturday, and Wenger hopes his side will be at their best to recover from Sunday’s loss at Old Trafford.
"We want to focus on the positives and recover from that defeat and give our best until the end of the season,” he said.
"I don't think we have any [injury] problems from Sunday, apart from one or two [with] muscular tightness, but everyone should be available."
Arsenal lie third in the English Premier League standings, five adrift of leaders Leicester City.
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