The England international has been sidelined since the opening day of the season when the Gunners slipped to a 3-1 defeat to Aston Villa.
Arsenal had initially tipped Oxlade-Chamberlain to make a return to first-team action within two months, but that timescale has now slipped a bit after his recovery from the injury stalled.
The 20-year-old has been ordered to rest up for the time being, in the hope of getting him back into training by mid-December.
Oxlade-Chamberlain is likely to have his work cut out to regain a starting berth for Arsenal once he is fully fit again following the arrival of Mesut Ozil at the Emirates Stadium, which could put his place in the England squad at next summer's World Cup in Brazil in jeopardy.
England boss Roy Hodgson is a big admirer of the former Southampton youngster, who scored in his country's 2-2 draw with the host nation in the Maracana last summer, but the emergence of Tottenham's Andros Townsend during his absence is certain to give him a selection headache.