MV Hondius, which has nearly 150 people on board, was expected to head next to Spain's Canary Islands, ship operator Oceanwide Expeditions said.
Three people have died in the outbreak.
South Africa confirmed it had identified among the victims the Andean strain of the virus that can - in rare cases - spread among humans.
Since the start of the outbreak, the WHO has said the risk to the wider public is low, and it stressed that this continued to be the case.
The Swiss government said a man who returned to Switzerland after being a passenger on the Hondius was infected with the hantavirus and was being treated in Zurich.
It said there was no danger to the broader population.
"Three suspected #hantavirus case patients have just been evacuated from the ship and are on their way to receive medical care in the Netherlands," WHO chief Tedros Adhanom Ghebreyesus said in a post on X on Wednesday.
The Dutch foreign ministry said those evacuated included a Dutch person, a German and a Briton.
They would be transported to specialised hospitals in Europe, it said.
Two of those evacuated presented acute symptoms, Oceanwide Expeditions said.
The third person was closely linked to the German passenger who died on the ship on May 2.
The Dutch ministry said that person was possibly infected with the virus.
A Dutch couple on the ship have also died, while a British national remains in intensive care in South Africa.
The Swiss case brings the hantavirus outbreak to a total of eight, three of them confirmed by laboratory testing, the WHO said, adding that it was helping countries with contact tracing to "ensure that those potentially exposed are monitored and that any further disease spread is limited".
Cape Verde had been intended as the ship's final destination, but the archipelago nation off West Africa has not allowed the passengers to come ashore because of the outbreak.
Late on Tuesday, the Spanish health ministry said it had agreed, in accordance with international law and humanitarian principles, to a request from the WHO and the European Union to allow the Hondius to dock in Spain.
Citing health ministry sources, the broadcaster TVE said that this would be in Tenerife.
The Spanish archipelago's leader Fernando Clavijo said he was opposed to the move and requested an urgent meeting with Prime Minister Pedro Sanchez.
People are usually infected by hantavirus through contact with infected rodents or their urine, their droppings or their saliva.
Human-to-human transmission is rare.
But a limited spread among close contacts has been observed in some previous outbreaks with the Andes strain, which has spread in South America, including Argentina, where the cruise trip started in March.
A presentation seen by Reuters said tests conducted by South Africa's National Institute for Communicable Diseases showed that the Andes strain was the cause of infection in the Dutch woman who died in Johannesburg as well as in the British man who is still in hospital there.
"This is the only strain that is known to cause human-to-human transmission, but such transmission is very rare and as said earlier, it only happens due to very close contact," the presentation said.
South Africa's health ministry has identified 62 contacts including flight crew and healthcare workers, but none has been diagnosed with the hantavirus so far.
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