The NBA all-star, set to play for France in the Olympics, reportedly got glass shards in his eye and suffered a scratched cornea.
Parker is out of action for at least a week, but is not expected to miss any time in the Games.
"I was there with a bunch of friends when a fight broke out," Parker said at a press conference. "They started to throw bottles about... I was lucky. The injury won't prevent me from competing the Olympics in any way."
Brown, his girlfriend and his bodyguard were injured in the dance floor showdown. Brown tweeted a photo of himself with a cut chin, then later removed it, as well as other messages about the fight, including epithets and taunts.
A representative later released a statement saying the singer and his girlfriend, model Karrueche Tran, were victims of a "brutal attack."
A representative for Drake said the star was on his way out of the club when the altercation began.
"He did not engage in any activity which resulted in injury to person or damage to property," according to the statement.
Meanwhile, the club where the brawl took place has been closed.
Police shut it down due to numerous violations.
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