Cook Islands Police Service spokesman Trevor Pitt confirmed the death, but did not specify the cause of the fatality.
He said a police investigation into the death was continuing.
“I can confirm that a team of police officers travelled to Mangaia on Sunday afternoon to investigate a fatality,” Pitt said.
“A Crown solicitor was part of the investigation team.
“Police are not yet in a position to comment on the cause or the actions which resulted in the death of a woman.”
The Cook Islands Police Service also asked people not to speculate the cause of the death as investigations were still underway.
However, it has been alleged that a couple were drinking when an argument broke out, resulting in the shooting incident.