The witness said the incident came out of the blue as the game had gone smoothly.
"The [attacker] was shouting, 'Why don't you referee the game properly?' ... It was outrageous behaviour and totally unacceptable in any sport and at any age."
Senior Sergeant Ian Brenchley of Counties Manukau police said a man was arrested.
Papatoetoe junior club delegate Rick Steedman said he had heard conflicting reports of the incident, one being that the referee was shoved in the shoulder.
"I did say to the guy, 'That's certainly not something that we condone.' And when the police have made their decision, the club will make a decision [on penalising the attacker] as well. And it's not going to be a favourable outcome."
Mr Steedman said nothing like this had happened at the club before and it made no sense given the teams' relationship.
He said the club was at a loss as to why tempers frayed so badly, given the teams had trained together for weeks.
"They are very close. They were forming one team at the start of the year, but because the numbers got so big they decided to take half each. All these kids and their parents have been one big group for 8-10 weeks."
After the attack, the children stayed on the field with their coaches while a group of parents and the two men walked to the clubhouse.
"The guy who was accused of assaulting the referee, he ... kept apologising, apologising, apologising," Mr Steedman said.
"As soon as I got involved, I just wanted to keep them apart and keep them quiet."
Last month, a player was arrested for breaking a soccer referee's jaw in three places after being sent off.
Referee Len Gattsche was attacked in the 79th minute of a division-two match between Manukau City and Tauranga City.
The sound of Mr Gattsche's jaw cracking was heard by spectators 40m away.
Tama Fasavalu, 36, was suspended from the game indefinitely and fined $1000 by the Auckland Football Federation.
