The Germany international did not travel with the squad for the fixture against Mark Hughes' side at the Britannia, prompting concerns over his fitness.
However, Wenger has now revealed that Ozil is expected to recover from the problem quickly, and he is expected to be back in time for next weekend's London derby against embattled champions Chelsea.
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"Mesut has a problem with his foot, an inflammation, but it's very short term - very short term," he told Sky Sports.
"He'll be back next week."
Alexis Sanchez was also left out of Wenger's team, not even making the bench, and the Frenchman says he did not dare rush the Chile international back and risk a lengthy lay-off.
“Because he was at 95 percent there, but with a muscular problem I didn’t want to take a gamble because if he has a setback now it’s three months," he said when quizzed about why he did not select the former Barcelona attacker.
"I think he’s a few days away so it was not worth the gamble.”