Health minister Ummy Mwalimu, who visited the area, said the disease was caused by a bacteria which spread through consuming water or food contaminated by infected animal urine.
"A good thing is that this disease is preventable and curable," she said, urging people to remain calm.
Last week authorities dispatched a team of doctors and experts to the southeastern region of Lindi where 20 cases have been reported, including the three people who died.
Most of the patients have recovered from the illness, whose symptoms include fever, headaches, fatigue and nosebleeds. Two people remain in isolation, she said.
All patients have tested negative for Ebola and Marburg, as well as Covid-19.
Tanzania's President Samia Suluhu Hassan said last week the "strange" disease reported in Lindi may have been caused by "growing interaction" between humans and wild animals as a result of environmental degradation.