It happened near the slopes of Mount Hanang, where President Samia Hassan has now deployed national security forces to help rescue efforts.
Homes and infrastructure were also damaged by the adverse weather.
Flooding is said to be the greatest natural hazard in Tanzania, affecting tens of thousands of people each year.
East Africa has been badly hit by floods and landslides in 2023, partly caused by the El Niño weather phenomenon.
Last month in Tanzania, higher than usual rainfall resulted in deaths and destruction to property in the capital Dar es Salaam and the areas of Kigoma, Kagera, Geita and Unguja.
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