Ozil, the club's record signing, was substituted at half-time during the 1-1 draw in the last 16 second leg at the Allianz Arena which saw holders Bayern progress 3-1 on aggregate.
Local media reported Ozil had sustained a hamstring injury though Wenger did not confirm that.
"It looks quite serious," said Wenger. "I don't know (how long Ozil will be missing) but for sure he is out (of the Tottenham Hotspur game on Sunday).
"We have to make a scan tomorrow to see how bad it is but he's out for at least a few weeks. I hope it's not too bad."
Ozil's injury came just as he appeared to be turning the corner following a run of misfortune. He scored the first goal in a 4-1 win FA Cup win over Everton on Saturday to end a three-month goal drought and gave a dynamic performance.
The German had looked jaded in the weeks before that and hit a personal low in the 2-0 Champions League home loss to Bayern last month, where he had his ninth minute penalty saved by international team-mate Manuel Neur.
Wenger dropped Ozil to the bench for the 1-0 league loss to Stoke City and he was booed by Germany fans in the friendly victory over Chile on week ago.
Arsenal are third in the Premier League seven points adrift of leaders Chelsea and six in front of fifth-placed local rivals Spurs who they visit on Sunday with a game in hand.
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