The crew members who tested positive were reported to be "doing well, with only mild symptoms," according to the ferry company.
The SeaDream Yacht Club vessel, which had 37 Americans aboard, returned to Barbados on Wednesday after the passenger tested positive.
The ship's itinerary hasn't changed following the tests.
The cruise began in Heraklion, the capital of the Greek island of Crete, and was due to sail to Piraeus, near Athens.
Hurtigruten's ship MS Roald Amundsen was one of the first cruise liners in the world to resume operations after they were halted amid the coronavirus pandemic.
A doctor on the Ruby Princess cruise ship allegedly told Josephine Roope that her friend had "only the flu, nothing to worry about."
Surface contamination can spread quickly, as a recent Japan Broadcast Corporation demonstration proves.
While Carnival Corporation confirmed it will "fully cooperate" with the investigation, Carnival Cruise Line announced it will resume voyages on eight ships from Miami, Port Canaveral and Galveston.
Among the ships are the Coral Princess, which announced Thursday that 12 people on board tested positive for COVID-19
As Carnival seeks $6 billion in funding to help with financial fallout caused by the COVID-19 pandemic, SEC filings on Monday showed that over 6,000 people were still sailing on ships owned by the company.
The cruise line has seen two of its ships report several confirmed cases of the COVID-19 virus since February.
"I'd rather have them stay on," Trump said Friday of people onboard a cruise ship where coronavirus was detected moored off the coast of San Francisco, "but I fully understand if they'd rather take them off."
Several major cruise lines—Royal Caribbean, Carnival, Celebrity Cruises and Crystal Cruises—have announced cancellations or changes to their itineraries for cruises in March and April.
More than half of those reported infected outside China were aboard the Diamond Princess cruise ship, which has been quarantined in Japan for over two weeks.
Frank King, a comedian who was working aboard the Holland America cruise ship that was quarantined after a former passenger tested positive for coronavirus, says that he was fired by the cruise line after sneaking out of quarantine and returning home to Oregon.
Authorities are scrambling to track the other passengers who were cleared for travel and allowed to disembark the MS Westerdam cruise ship after showing no signs of illness.
At least 1,500 people have died of the coronavirus since it first emerged late last year.
A Holland America Line cruise ship has been unable to dock for almost two weeks, despite having no reported cases of the virus.
The new form of the coronavirus has killed over 910 people since it emerged in China late last year.
The new strain of coronavirus has killed over 550 people since late last year.
The ship will remain in quarantine for at least another two weeks, as required by the Japanese government.
Thousands of passengers and crew members on board the Diamond Princess cruise ship have been quarantined off the coast of Yokohama, near Tokyo, Japan.
Pua Morrison said she and seven family members paid $4,000 each for a cruise with Norwegian Cruise Line that departs in the next couple of days and stops in Hong Kong.
A Carnival Cruise Line spokesperson has confirmed the victim was an 81-year-old woman, with the cause of death currently believed to be natural causes.
Around 6,000 passengers aboard the Costa Smeralda have been locked down in the Italian port of Civitavecchia.
The passenger fell from the deck of the Oasis of the Seas ship while it was in San Juan Bay in Puerto Rico.
We realized this was a time sensitive case, and that we needed to help this child get to a higher level of medical care as soon as possible," Petty Officer 2nd Class Carlos A. Garay explained.
Rebecca Kaplan said she contacted a cruise ship company about docking a vessel at the Port of Oakland to house as many as 1,000 homeless people.
Chloe Wiegand fell to her death from aboard the Royal Caribbean's Freedom of the Seas in July while it was docked in Puerto Rico.