Nauru President Lionel Aingimea has expressed his condolences and sympathies for the family via a video statement.
More than 4000 cases have been recorded in the community since the outbreak was announced just over two weeks ago.
There are 3838 active cases in the community as of Saturday night, and 229 people have recovered.
In Niue, the number of active Covid-19 cases at the border has hit ten.
It follows the arrival of the first quarantine-free flight from New Zealand last week.
The government said, so far, all of the people who have tested positive for the virus were on the flight.
Premier Dalton Tagelagi is a close contact of one of the passengers and is in isolation at home.
Niue remains at alert level yellow as there is no community transmission of the disease.