Spokesperson Trevor Pitt said the incident took place at around 5am when a fight broke out near Raro Fried Chicken.
Later that morning a male had arrived at the police station to admit that he had been involved in the incident, Pitt said.
He said the man’s injuries did not appear to be serious but he was advised to get medical treatment.
Three other fights were reported to police that morning and late on Friday night.
Pitt said the festive season was always a busy time for police officers in Rarotonga as they attended an increasing number of callouts.
On Friday night two people were arrested for dangerous driving, a woman is facing a drink-driving charge and a man was charged with obstructing police.
A driver was forbidden to drive before 1am, after police were called out to a crash at Betela. The driver of a motorbike sustained a broken leg after crashing into a rail near the meeting house.
A woman pedestrian was injured when she was struck by a motorcycle on the Arorangi main road on Saturday morning.
Pitt said both the woman and the motorcycle rider required medical attention and were admitted to hospital. The man sustained serious head and leg injuries while the woman suffered leg injuries and neck pain.
Police believe the incident was alcohol-related.
On that same morning, three people appeared in court on drug-related charges.
Meanwhile, phones and a large amount of cash were taken during a break-in at Tupapa.