Ozil was substituted at half-time in Tuesday night's Champions League last-16 second-leg tie at the Allianz Arena with a hamstring problem.
The Germany international midfielder has been in indifferent form in recent weeks but the news is another blow to Arsenal's Premier League title hopes.
Last week, Jack Wilshere was ruled out for around six weeks after suffering a foot injury whilst playing for England.
On the loss of Ozil, boss Arsene Wenger said: "It looks quite serious.
"I don't know (how long he will be out for), but for sure he is out (of the Tottenham 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."
Arsenal were only able to name six substitutes in Munich, with midfielder Ryo Miyaichi part of the travelling group following some late withdrawals, but it was later discovered he was not eligible for the pre-submitted Champions League squad.
"He was not eligible because he was not qualified to play in the Champions League because I wanted to give him out on loan, so we took him out of the list and UEFA informed us today that he is not qualified," said Wenger.
"Because he was on the bench on Saturday (against Everton), naturally he was with us but honestly that did not have an impact on tonight's result."