Ozil, a German Muslim of Turkish origin signed by Wenger in 2013, posted messages on Twitter and Instagram last week calling minority Uighurs "warriors who resist persecution".
Arsenal's Ozil condemns Muslim silence over Uighurs
China's foreign ministry said Ozil had been deceived by fake news as the country's Twitter-like Weibo platform erupted with angry messages, some calling for the London club to sack their highest-paid player.
Wenger told reporters in Doha he did not know if there would be a long-term impact for Ozil.
"I don't think the situation is definite, that can change very quickly, and although I don't know the situation well overall, Ozil made a comment and after, when you make a comment about your individual opinion, you accept the consequences of it," Wenger said.
"First of all Mesut Ozil has freedom of speech like everyone else and he uses his notoriety to express his opinions, what is not necessarily shared by everybody but he has the right to do that," the Frenchman added.
US Secretary of State Mike Pompeo came out in support of Ozil on Tuesday, saying Beijing could not hide rights violations.
China has repeatedly denied any mistreatment of Uighurs. But the United Nations and rights groups estimate up to two million mostly ethnic Uighur Muslims have been detained as part of what Beijing calls an anti-terrorism campaign.
Chinese TV pulls Arsenal match after Ozil's Muslim Uighur comments
Arsenal was quick to distance itself from their midfielder's comments, posting a statement on Weibo saying it was his personal opinion. Wenger said he did not want to get involved in the debate about the right balance between players' opinions and the commercial relationships big clubs, such as Arsenal, have internationally.
"I don't want to go into that dilemma, I think what is important is that Ozil has an individual responsibility, he doesn't carry the word of Arsenal Football Club. So what he says is about himself, not about Arsenal," Wenger added.
The National Basketball Association says it has incurred substantial financial losses in China since a Houston Rockets official tweeted his support for Hong Kong's pro-democracy protests in October.
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