The 29-year-old miner died on July 14, one week after he was hospitalised in the west of the country, WHO spokeswoman Fadela Chaib said. The disease was only diagnosed on Monday.
Ugandan authorities have informed the WHO of two other suspected cases, Chaib said.
"For the moment, there is no reason to be alarmed. The Ugandan health ministry has done what it can. But we are concerned because there is no vaccine or treatment against the Marburg disease which, if it spreads, can kill very quickly," she said.
Another miner who had been in contact with the deceased man had also contracted similar symptoms but has now left hospital.
The disease takes its name from the German town of Marburg, where it was first detected, in 1967, among lab workers who were infected by monkeys from Uganda.
It spreads through contact with blood, excrement, vomit, saliva, sweat and tears. The natural reservoirs for Marburg, and its notorious cousin Ebola, are in the African tropical forest, but the precise animal source remains unknown.
Two recent major Marburg epidemics caused hundreds of deaths in Africa.
The first killed 128 people in the Democratic Republic of Congo between 1998 and 2000, and the second left 150 dead in Angola between 2004 and 2005, according to the WHO.