The teenager was remanded into custody on Monday after appearing in court on a charge of manslaughter.
The young man was arrested on Sunday following the incident on late Saturday night.
In a statement, Cook Islands Police said the two men, who were known to each other, were alleged to have been involved in a dispute which resulted in the death of the 25-year-old.
At a court appearance on Monday, no plea was taken.
The defence counsel opposed a request for remand but the court approved the application by the police prosecution, police said.
The defendant will be in custody until reappearing in court on January 18.
In an earlier statement police said they were not seeking anyone else in connection with the incident.
Criminal Investigation Bureau officers were continuing with their investigation, which was being treated as very serious, the statement said.
“Police will provide appropriate information in due course. Until then, please limit any (social media) comments and exercise sensitivity for the families involved. Any posts deemed unsuitable will be removed immediately.
“Please also have consideration for the police officers, who must fulfill their duties under difficult conditions, irrespective of the timing or otherwise of such incidents.” - RK/Release