Tamaki College refused to comment.
Police said officers visited the school after the altercation between the two teams.
"We are not aware of any injuries in relation to this matter and no person was arrested."
"At the time police were attending the incident, an 18-year-old male was arrested unrelated to the fight for wilful damage and has been referred to Te Pae Oranga."
Auckland Rugby said it had received a match report from the game and was now investigating.
"Auckland Rugby is committed to providing a safe and enjoyable experience for all of our rugby whanau," a spokesman said.
"However, at this stage, we are not in a position to comment further."
The brawl comes after a spate of violence across the country against rugby referees.
Otago player Vaea Uelese, 27, last week appeared in the Dunedin District Court charged with assaulting referee Brandon Hale at a country footy game on July 27.
Witnesses at the match said the referee penalised Uelese's team Crescent Rugby Club after a player in the game against Strath Taieri in Middlemarch barged into an opponent who was picking up the ball to take a penalty.
Video footage taken from the sideline showed the official bringing out the offending Uelese and the Crescent captain.
After briefly speaking to them, the referee showed Uelese a red card for his actions.
He then allegedly punched the referee, hitting him in the shoulder and then his head.
After a short melee, the game was then called off.
In another incident in Auckland, a young rugby referee was punched and strangled by a spectator after he sent a player off the field at an under-12s game.
A witness to the 9am home game, between the blue and red Ardmore Marist teams at Auckland's Pulman Park in late July, said the 15-year-old referee had warned the player three times before sending him off.
After the final whistle, a spectator - who appeared to be related to the player - approached the referee to speak with him.
Following their discussion. "the young ref went to walk away and was blindsided by a hit to his chin that landed him on the ground", the witness said.
The spectator "then tried strangling him - picking the ref up by the throat".
Other parents quickly ran on to the field to intervene.
Police said at the time they would investigate the assault.