The Germany international was withdrawn at half-time in the UEFA Champions League loss at the Allianz Arena after sustaining the problem.
Manager Arsene Wenger confirmed on Friday that the club's record signing could be out for as long as six weeks - a blow to Arsenal as they challenge for the Premier League and FA Cup titles.
"Ozil will be out for three weeks," the Frenchman initially said, before adding: "When the minimum is three, the maximum is six so let's say four weeks."
Wenger continued: "It's a blow to lose Ozil but I'm confident we have the quality to deal without him. We have many good players in our squad."
January signing Kim Kallstrom could make his debut in Sunday's derby against Tottenham after overcoming a back complaint, but that game will come too soon for Aaron Ramsey, who has yet to fully recover from a thigh injury.
"(Ramsey) still has recurrent pains in his thigh, we have to be very cautious with him," explained Wenger.
"Kallstrom is back in the squad and will be available for Sunday."
Arsenal's boss also distanced himself from reports in Spain suggesting he could replace Gerardo Martino as Barcelona coach.
"My commitment is here and nowhere else," said Wenger.
