Cook Islands, a small South Pacific nation that has not experienced Covid-19 in its community, is readying for its first coronavirus infections after an infected traveller visited, Prime Minister Mark Brown said on Sunday.

The traveller from New Zealand spent eight days in the community and tested positive for Omicron upon returning home last week, Brown said in a video posted on the government's Facebook page.

"It is likely that the person … was infectious while here and further likely that the virus is in our community," he said.

"It may be there is 'silent transmission', where our high vaccination rate is so protective that people get Covid but so mildly that they do not realize they have it."

Official data show that 99.6% of the island nation's roughly 17,000 people aged 12 and over is double-vaccinated, and 70% of those eligible have had their booster shots.

Cook Islands resumed quarantine-free travel with New Zealand a month ago, after shutting itself off from the world when the pandemic hit in early 2020.

In December, the country reported one case of Covid-19 in a person quarantining after arriving on a repatriation flight, who was not exposed to the community.

"The fact that we have a high percentage of our people vaccinated will give us substantial protection from serious illness," Brown said.