Prime Minister Mark Brown said this case was not connected to the visitor who tested positive for Omicron after leaving Rarotonga and arriving back in New Zealand last Monday.
He said this person - who is currently isolated and under observation at their private holiday accommodation - arrived in Rarotonga last Thursday.
They were a close contact of a family member in Auckland who tested positive on Sunday in New Zealand.
Brown said as a precaution this person got tested, and was asymptomatic, but she returned a positive result in just a few hours later.
The woman is travelling with two others, and they will all remain in isolation until they no longer test positive for Covid-19.
Brown said it was helpful that the person was staying in private holiday accommodation, not a resort or motel.
The woman was double vaccinated and had returned a negative PCR test prior to boarding their flight from New Zealand.
In his nationwide address Brown had pertinent advice for Cook Islanders: "Our extremely high vaccination rate is another factor in our favour, as it slows the spread of transmission and reduces the health impacts in those who do contract this virus.
"I can also tell you that from the moment Te Marae Ora confirmed this person as testing positive for Covid-19, our contact tracing team swung into action to trace their movements since arriving in Rarotonga and to start identifying any potential close contacts."
Brown said locations of interest would be available on the Covid-19 website and the TMO Facebook page.
"As each new piece of information is gathered and confirmed, we will also be keeping you all as up-to-date as possible as any new places of interest and potential close contacts are identified.
"Those people deemed to be close contacts of this case are currently being contacted by TMO and will be advised to get tested." - RNZ
Photo/RNZ/Nate McKinnon Caption: Cook Island Prime Minister Mark Brown.