The Cook Islands Government says the contact between the family member and the recent arrival from New Zealand was "brief and apparently unintentional" - but the entire family will now be moved to a supervised quarantine facility for the next two weeks.
"The person he had contact with had returned a negative Covid-19 test before leaving New Zealand, and has had another test in-country this afternoon which has returned negative, and is not showing any Covid-19 symptoms," the Government said in an online post.
"The man who entered the supervised quarantine property also tested negative this afternoon for Covid-19."
The Cook Islands remain Covid-free, however community leaders have voiced concern that an outbreak could overwhelm its health system.
Strict quarantine protocols are in place for people who have returned to the Cook Islands from overseas, including a ban on physical contact with people in supervised quarantine or those in properties displaying yellow flags.
Dr Aumea Herman, Secretary of Health, said the "unfortunate" breach of quarantine orders was a lesson for all to remain vigilant.
"The person in quarantine was in the right place and obeying the rules, including wearing a mask; there was a yellow flag outside the property indicating there were people in quarantine there," he said.
"Largely because of the actions of the person who returned on Friday, the public health risk from this incident is very low. However we are taking precautionary measures to ensure the safety of the family involved and members of the public."
A community leader in the Cook Islands recently urged the New Zealand government to offer more guidance on what should be done in case of a Covid-19 outbreak.
Cook Islands Private Sector Task Force head Fletcher Melvin told RNZ the Cook Islands felt prepared for an outbreak, but community leaders wanted to be sure everything was up to scratch.
Dr Joe Williams, a former Prime Minister of the Cook Islands and a much-respected GP, died on Friday from the virus.
The widely-respected medical professional becomes the 24th person in New Zealand to die from Covid-19 and the second in less than 24 hours related to the current Auckland cluster.
Williams was admitted to Auckland City Hospital on August 13.
