That's in addition to 85 injured in the Manyara region.
Search and rescue operations are underway, Manyara region commissioner Queen Sendiga told reporters, amid fears that some bodies might be trapped in the mud.
President Samia Suluhu Hassan said that in the village of Katesh, in Hanang district, 100 houses had been swallowed by a landslide.
"I want to say that I have instructed that all efforts are directed towards rescuing those who were involved in this tragedy and to prevent more deaths."
Tanzania's disaster follows hundreds of deaths in Somalia and Kenya since seasonal rains began in October.
A combination of the El Nino and Indian Ocean dipole weather phenomena has caused severe flooding that has also forced hundreds of thousands from their homes.
Scientists say climate change is causing extreme weather events that are more intense and more frequent.
