May underwent surgery on Saturday to insert two plates into his left jaw, which was broken in an altercation with Brown in Los Angeles earlier this week.
The incident happened at the end of the Suns' 18-day Arizona altitude training camp on a night out.
Gold Coast chairman John Witheriff wrote an open letter to supporters on Sunday that said Brown "understands the suspension and is cooperating fully with the on-going investigation".
Jaw surgery for May
Following a full board meeting on Thursday, it was decided club CEO Travis Auld and football manager Marcus Ashcroft would conduct a detailed investigation into the incident.
The board has delegated its authority to make a decision on the matter to Witheriff and fellow board member Bob East.
Witheriff emphasised that due to the seriousness of the matter, which could end Brown's 205-game career, the thorough investigation would be allowed to run its course.
"As you would expect, their brief has been to gather all the relevant facts, ensuring that any ruling the club makes will be made with accurate and substantiated information," Witheriff said in the letter published on the club's website.
"This is being done in a timely manner, but I must stress that the board is committed to a fair and appropriate outcome.
"The integrity of the investigation is my dominant concern."
The Suns believe May will be able to resume running in about two weeks.
A number of players who were present at the time of the incident will be spoken to as part of the investigation.
It has been reported Hawthorn premiership player Josh Gibson was also present at the time May was injured.
Witheriff said the club was determined to reach "a fair and appropriate outcome for all involved", and pledged to keep the Suns' supporter base informed throughout.
"As chairman of the Gold Coast Suns, I share the high expectations you have of our club," he said.
"The club will continue to keep our members and supporters updated and will provide you with further information at the appropriate time.
"In the meantime, rest assured, we are committed to a fair process, that will reflect the values of our club - its members, players, staff and sponsors."
Twitter: @AFL_JenPhelan
Following a full board meeting on Thursday, it was decided club CEO Travis Auld and football manager Marcus Ashcroft would conduct a detailed investigation into the incident.
The board has delegated its authority to make a decision on the matter to Witheriff and fellow board member Bob East.
Witheriff emphasised that due to the seriousness of the matter, which could end Brown's 205-game career, the thorough investigation would be allowed to run its course.
"As you would expect, their brief has been to gather all the relevant facts, ensuring that any ruling the club makes will be made with accurate and substantiated information," Witheriff said in the letter published on the club's website.
"This is being done in a timely manner, but I must stress that the board is committed to a fair and appropriate outcome.
"The integrity of the investigation is my dominant concern."
The Suns believe May will be able to resume running in about two weeks.
A number of players who were present at the time of the incident will be spoken to as part of the investigation.
It has been reported Hawthorn premiership player Josh Gibson was also present at the time May was injured.
Witheriff said the club was determined to reach "a fair and appropriate outcome for all involved", and pledged to keep the Suns' supporter base informed throughout.
"As chairman of the Gold Coast Suns, I share the high expectations you have of our club," he said.
"The club will continue to keep our members and supporters updated and will provide you with further information at the appropriate time.
"In the meantime, rest assured, we are committed to a fair process, that will reflect the values of our club - its members, players, staff and sponsors."
Twitter: @AFL_JenPhelan
