Van Kerkohve said that the WHO's "top priority" remained treating the two crew members who were on board with respiratory symptoms.
They are due to be medically evacuated via aircraft to the Netherlands, alongside a person "associated" with the German national who died, according to Oceanwide Expeditions.
Nobody else on the ship has shown symptoms.
Though human-to-human transmission of hantavirus is rare, van Kerkhove told BBC Breakfast some could have taken place between close contacts sharing cabins.
Hantavirus first could have been contracted from rodents before the ship embarked from Ushuaia in Argentina, or on one of its stops along the way, she added.
She noted the cruise went to many different islands, some of which have rodents.
"Our working hypothesis is that there's probably a couple of different types of transmission that might be happening," van Kerkove said.
MV Hondius during a trip from Argentina to Antarctica via South Georgia
MV Hondius during a trip from Argentina to Antarctica via South Georgia in November 2021
One passenger, who asked to remain anonymous, told the BBC: "The latest word is that a plane is on its way and once it gets here three people will be evacuated from the ship and flown straight to Europe.
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