Jane Ruth Aceng told reporters on Thursday that the case had been confirmed after a series of tests were carried out.
The East African nation last suffered a Marburg outbreak, which has a high mortality rate, in 2014. Marburg is from the same family of viruses as Ebola, which killed thousands in West Africa in 2014.
The victim, a 50-year old woman, died on October 11 at a hospital in eastern Uganda after “she presented with signs and symptoms suggestive of viral hemorrhagic fevers,” the minister said.
The woman had nursed her 42-year old brother who died on September 25 with similar signs and symptoms and also participated in cultural preparation of the body for burial, she added.
Aceng said the man was “a hunter who carried out his activities where there are caves with heavy presence of bats,” Aceng said.
The African fruit bat is the reservoir host of the Marburg virus although infected bats do not show obvious signs of the disease.
Symptoms and signs of Marburg include headache, vomiting blood, muscle pains and bleeding through various orifices. Transmission of the disease occurs through contact with infected blood or other body fluids and tissue.
The World Health Organization (WHO) says it has deployed staff in Uganda to bolster efforts to contain the outbreak.
Uganda has suffered several outbreaks of Marburg and Ebola in the past, although they have been mostly contained quickly which has limited fatalities.
The country’s worst occurrence of a hemorrhagic fever was in 2000, when 425 people contracted Ebola and more than half of them died.
Marburg’s fatality rate, according to WHO, has varied over the years with the highest, 80 percent, occurring in outbreaks in the Democratic Republic of the Congo between 1998-2000 and in Angola in 2005.