The 63-year-old woman died on the way to hospital on the island of Aitutaki, Prime Minister Mark Brown said in a statement.
"It is with great sadness that I announce that we have recorded our first in-country death attributed to Covid-19," Brown said.
"The deceased was a 63-year-old woman on the island of Aitutaki.
"She had had all three anti-Covid vaccinations, but also had several serious underlying health conditions."
"It is tragic, but not unexpected that we might lose someone to Covid.
"I, together with Te Marae Ora [Ministry of Health], am sending our condolences to the family who have just lost a loved one, our thoughts and prayers are with them at this time and the people of Aitutaki."
Rarotonga reported 73 new cases of Covid-19 in the 24 hours to yesterday morning, while Aitutaki reported 43 cases.
The Cook Islands have had a total of 4727 cases, 3990 of whom have recovered.
Earlier in the weekend Mr Brown had said given the improving situation on Rarotonga and Aitutaki the government has made changes.
He says from next Sunday travel to Aitutaki will be unrestricted, meaning no pre-departure RAT tests, and unvaccinated people will also be able to travel there.
The islands had their first case of Covid-19 detected only in February, far later than much of the world.