Tanzania's President Samia Suluhu Hassan said the "strange" disease may have been caused by "growing interaction" between humans and wild animals as the population pushes further into the bush.
The news from Tanzania comes days after the World Health Organisation announced that Ghana has reported two possible cases of Marburg, which if confirmed would mark the first-ever such infections in the West African country.
The WHO said the disease is spread to people by fruit bats and transmitted among people through direct contact with bodily fluids of infected people and surfaces.
It is potentially very harmful and deadly: Case fatality rates in past outbreaks have ranged from 24 per cent to 88 per cent.
"Preparations for a possible outbreak response are being set up swiftly as further investigations are underway," the WHO said, adding that it is deploying experts to support health authorities in Ghana.
The WHO said that if confirmed as Marburg, the cases would be the second time that the disease has been detected in West Africa - after Guinea confirmed a single case last year.
- Additional reporting, AP