Parker said he suffered a scratched cornea on his left eye from broken glass during the brawl.
The suit, filed in New York Supreme court on June 21, claims the W.i.P club and its operators were negligent in security and supervision by allowing the fight to take place.
In the complaint, Parker accused the club of being reckless for "sitting persons known to be hostile to each other at the same time in order to generate funds for themselves." He also claimed the club served "visibly intoxicated" persons alcohol and allowed "criminal and other improper activity."
Brown, his girlfriend and his bodyguard were among eight people injured during the fight inside the club last week. Police said members of Drake's entourage got into a fight with Brown's group as they were leaving.
Witnesses say it all started after two men approached Brown's table and asked him whether he had a problem with Drake, and he said, "No." According to police, bottles started flying.
Neither Brown nor Drake were at the club when police arrived around 4 a.m. The reason behind the fight remained unclear, but both musicians dated singer Rihanna at one time.
Drake has denied any wrongdoing.
"He 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," Drake's representative said in a written statement.
The club was shut down a few days later and the manager was arrested on two outstanding warrants unrelated to the brawl.
The Associated Press contributed to this report.