The former Hawthorn premiership winner learned his fate after the AFL club completed their investigation of last week's incident outside a Los Angeles nightclub, following Gold Coast's pre-season camp in Arizona.
Brown was suspended on Sunday when the club began their probe.
May returned home to Australia and needed two plates to repair the break in his left jaw and was expected to return to training in a fortnight.
Hawthorn star and Brown's former teammate Josh Gibson was also understood to have been with the group of Suns players when the incident happened.
Brown already was set to miss the opening round of next season because of suspension.
It was not the first time the Suns veteran had landed in hot water during an end of season trip.
He was dumped from the Gold Coast leadership group for his part in a Thailand bar-room brawl in September 2011.
Brown - then the Gold Coast deputy vice-captain - was among four Suns players involved in a fracas at an infamous full moon party on the island of Koh Phan Gan.