A Dutch couple and a German national had died, while a British national was evacuated from the ship and is in intensive care in South Africa, officials said.
Three more suspected cases affect people who are still on board, one of whom has a mild fever.
The UN health body said its working assumption was that the initial case of the couple, who joined the boat in Argentina, were infected off the ship, perhaps while doing some activities such as bird watching, and that human-to-human transmission might have happened on board.
The cruise ship hit by the deadly outbreak is marooned off Cape Verde - an island nation in the Atlantic off West Africa - and not allowed to put passengers ashore.
The WHO said the focus was to evacuate the two sick passengers onboard to the Netherlands and then for the ship to continue to the Canary Islands.
Human-to-human transmission is uncommon, and the WHO reiterated that the risk to the wider public was low from a disease typically spread from infected rodents that only rarely passes between humans.
People are usually infected by hantavirus through contact with infected rodents or their urine, their droppings or their saliva.
However, a limited spread among close contacts has been observed in some previous outbreaks with the Andes strain, which the WHO believes could be involved in this instance.
"We do believe that there may be some human to human transmission that's happening among the really close contacts, the husband and wife, people who have shared cabins," Maria Van Kerkhove, the director of epidemic and pandemic preparedness and prevention at the World Health Organisation, told reporters in Geneva on Tuesday.
"Some people on the ship were couples, they were sharing rooms so that's quite intimate contact."
Van Kerkhove said the agency's working assumption was the hantavirus on the ship was the Andes virus, which spread in South America, including Argentina, and that testing was under way.
The Hondius left Ushuaia in southern Argentina in March.
Anyone symptomatic on the ship and those caring for patients were wearing full personal protective equipment, with extra supplies having been brought on to the boat, Van Kerkhove stated.
The WHO said it had been told there were no rats on board.
While the WHO said the ship would be headed to the Canary Islands, Spain's health ministry said it had made no decision yet on receiving it.
About 150 people are stuck on the Hondius, which was carrying mostly British, American and Spanish passengers on a luxury cruise that set off from the southern tip of Argentina in late March.
The cruise visited the Antarctic peninsula and South Georgia and Tristan da Cunha - some of the remotest islands on the planet.
The first stricken passenger, the Dutch man, died on April 11.
His body remained on board until April 24, when it "was disembarked on St Helena, with his wife accompanying the repatriation", Oceanwide Expeditions said.
His wife, who had gastrointestinal symptoms when she was disembarked, later deteriorated during a flight to Johannesburg.
She died on arrival at the emergency department on April 26, the WHO said, adding that contact tracing was under way for passengers on that flight.
South African authorities have confirmed that the British patient, who is being treated in a Johannesburg hospital, tested positive for the hantavirus.
The Netherlands has confirmed the virus in the Dutch woman who died.
