The Germany midfielder was replaced by Tomas Rosicky at half-time in the 1-1 second-leg draw at the Allianz Arena on Tuesday, a result that ensured defending champions Bayern progressed to the quarter-finals 3-1 on aggregate.
Arsenal manager Arsene Wenger revealed that his club record signing is now set for a spell on the sidelines, which is a major blow for the London club as they attempt to stay in the race for the Premier League title.
Wenger said of Ozil: "It looks quite serious. For sure he's out for at least a few weeks."
Trailing 2-0 from the first leg, the London club never looked like repeating their stunning 2-0 victory at Bayern last season as they were second best throughout.
Bastian Schweinsteiger put the European champions in front 10 minutes into the second half, but Lukas Podolski equalised with a controversial goal two minutes later after he appeared to push Philipp Lahm.
The Bavarian giants could have won on the night in stoppage-time, but Thomas Muller's penalty was saved by Lukasz Fabianski after Laurent Koscielny had brought down Arjen Robben.
Robben had earlier gone down easily in the penalty area, but referee Svein Oddvar Moen waved play on and the Netherlands winger also won the penalty that resulted in Wojciech Szczesny being sent off in the first leg.
Wenger accused Robben of diving in the first leg and the Frenchman was unimpressed with the former Chelsea man again in the second leg.
He said: "Robben is very good at getting the maximum of nothing,
"He is a great player, but also a good diver.
"He gets past the player, then he actually slows down, looking for the foul."
