The alert level remains unchanged and the risk to public remains low, the government said.
The man who arrived in Auckland from Egypt on May 5, 2021, and tested positive on his Day 0 test when in managed isolation (MIQ) in Auckland, according to a statement issued by Te Marae Ora Ministry of Health.
The Health Ministry said the man was asymptomatic and his test was deemed a historic case. As of Saturday evening, he remains asymptomatic.
According to the Ministry, a historical case means such cases are no longer infectious.
Because he needed to have a COVID-19 test before returning to Egypt, he requested one late Friday and the result came back positive. The man was not showing any symptoms of the disease.
In a statement, Secretary of Health Bob Williams said Te Marae Ora staff acted with urgency late last night and have taken this matter very very seriously.
At 11.30pm Friday night upon confirmation of a positive test result, the Health Intelligence Unit was activated, and staff recalled.
Investigations took place to find out whether this person was infectious, where he had been and his travel history.
Between 1am and 6am Saturday morning the man, his wife, son, and nine close contacts were all tested and were self-isolating while the tests were processed.
The man was also tested again and again he returned a positive result.
His wife, son, and close contacts have returned negative test results, and no-one has been required to self-isolate.
"Our systems have been tested and have worked and I am confident with the results," said Williams.
"Indications are that the positive test has reacted to an historical infection of COVID-19. Overseas, people have been known to continue testing positive for the virus for some considerable time after they have recovered from it and are no longer infectious."
"The Cook Islands Police are presently investigating the matter in relation to the information the man provided in his arrival health declaration form," Williams added.
The country remains at Alert Level 1.