The NBA star was at W.i.P in New York on Wednesday (June 13) when a physical fight broke out and bottles were thrown.
According to TMZ, Parker was taken to hospital with shards of glass in his eye.
"I was there with a bunch of friends when a fight broke out," Parker explained. "They started to throw bottles about. I got it all.
"The cornea has been touched. I can't do anything for seven days. But I was lucky. The injury won't prevent me from competing in the Olympics in any way."
Parker was scheduled to join the French Olympic basketball team for preparations on June 20.
Brown has reportedly spoken to detectives about the W.i.P. incident. Drake has denied being involved in any wrongdoing.
A group known as WE MOBBIN DVD has claimed that it has "the whole fight on camera" and will be selling it on DVD.
Watch a preview of the apparent 'fight' DVD below: