The disease, known as Marburg virus disease (MVD), is similar to Ebola and can be lethal in up to 90 per cent of cases.
Emergency screening has begun at the Kenya-Uganda border in Turkana after three members of the same family died of the disease in Uganda.
The outbreak is thought to have started in September when a man in his 30s, who worked as a game hunter and lived near a cave with a heavy presence of bats, was admitted to a local health centre with a high fever, vomiting and diarrhoea.
He did not respond to antimalarial treatment and his condition rapidly deteriorated.
He was quickly taken to another hospital in the neighbouring district, but died shortly after arriving.
His sister, in her 50s, died shortly afterwards and a third victim passed away in the treatment unit of a local health centre.
The WHO website reads: “Marburg virus disease is a rare disease with a high mortality rate for which there is no specific treatment.
“The virus is transmitted by direct contact with the blood, body fluids and tissues of infected persons or wild animals (e.g. monkeys and fruit bats).”
Several hundred people are believed to have been exposed to the virus, which is among the most virulent pathogens known to infect humans.
Early symptoms include fever, chills, headache, and myalgia.
The news comes as Madagascar faces a deadly outbreak of plague, which has already claimed the lives of 127 people.
Cases of the plague have soared in recent days and extra funding has been released by the World Bank to provide additional resources in the face of the “worst outbreak for 50 years”.
The outbreak has been compared with the Black Death, when plague swept across Europe and Asia in the 13th century, killing more than 50 million people in what is now considered one of the worst pandemics in human history.
Two thirds of the recorded cases in Madagascar are caused by the pneumonic plague, which can be spread through coughs and sneezes and without treatment, can kill within 24 hours.
The outbreak has prompted warnings that it could spread to nine nearby countries, including UK holiday hotspots Mauritius and the Seychelles.