"Police believe that at this point the coach of the Norths team punched the coach of the Para Plim team once in the head.''
Shortly after the two were separated by parents from both sides, a Norths supporter assaulted the parent of one of the Para Plim players.
Police charged the coach of the Norths team, aged 43, and the Norths supporter, 35, with common assault.
They will appear in the Porirua District Court tomorrow morning.
Mr Tunley said the Porirua community was shocked.
"These incidents are are very rare in Porirua.
"We don't like to hear of parents even arguing on the sidelines in front of their children, let alone assaulting people,'' he said.
Witnesses at the game have said the fight was racially motivated.
One spectator wrote on the Northern United Rugby Football Club's Facebook page on Saturday afternoon that a Para Plim parent had used a racial slur against the referee, resulting in a "fight between parents on both sides''.
"What I viewed was unprofessional by one Para/Plim parent and he should be banned from all rugby!
"The kidz are only under 11 and wanted to play,'' Rodney Betham wrote.
Tunley said he was not aware of any racial slur, but that it would be investigated.
Both clubs said they were taking the incident seriously.
Norths junior convenor Andrew Scott said officials were not ruling out banning members involved in the fight from future games.
"The club is taking this incident very seriously. Violence is not tolerated in any shape or form and will be dealt with.''
Para Plim president Mike Barry said the club was still deciding how to deal with members that were involved because it was a first for the club.
He expected a club meeting to be held tomorrow night after the duo's court appearance.
Wellington Rugby Football Union spokeswoman Bronwyn Williams said the organisation and its member clubs did not condone acts of violence on or off the field.
"Together with the two clubs involved we will act to ensure appropriate measures are taken once the matter is dealt with by the police. Wellington Rugby remains committed to ensuring that children, parents, coaches and spectators are able to enjoy the game.''
The Wellington Rugby Referees Association was not immediately available for comment.