David Panuelo last week announced the sailor on the government ship, MV Chief Mailo, had tested positive after it returned from the Philippines.
He said the ship and its crew are isolated in the Pohnpei lagoon under heavy watch.
In a national address, Mr Panuelo said the crew was tested before they left the Philippines, and he allowed them to return because they feared for their safety.
"The crew was rightly fearful of increasing numbers of pirates in the region which contributed to their fears. So I could either abandon the ship that the government uses to service the state of Chuuk and leave its crew and the 12 year-old boy from Poluwat outside of our care or I could bring them home."
David Panuelo said the country's first case of Covid-19 poses little risk to the community.
Mr Panuelo said the case is in well-contained border quarantine.
"The individual with Covid-19 on the Chief Mailo does not present any immediate risk of the virus spreading to the broader community in Pohnpei," he said.
The president said there is currently no need to change alert levels, schools remain open while mask-wearing and social distancing is only encouraged, not mandatory.
The country has so far received more than 9-thousand doses of coronavirus vaccine from the US, with inoculation programmes already underway.