Zuhura Yunus, spokesperson for President Samia Suluhu Hassan's office said in a statement that the landslides and floods had affected 1,150 households, or 5,600 people.
Severe flooding caused by El Nino and the Indian Ocean Dipole weather phenomena has killed hundreds of people in Kenya, Somalia and Ethiopia, and forced hundreds of thousands from their homes since seasonal rains began in October.
Yunus said Hassan would shorten her trip to the COP28 climate talks taking place in the United Arab Emirates and return to Tanzania to oversee the response to the incident.
"Despite all the challenges rescue work is facing from damaged roads and mud and logs filling the roads, the government is doing its best to deal with that," Yunus said.
Manyara region commissioner Queen Sendiga told reporters late on Sunday that the death toll stood at 47, with another 85 people injured.
Search and rescue operations were underway in the Manyara region as authorities fear some bodies might be trapped in the mud, she said.
Around 100 houses in the village of Katesh, Hanang district, were swallowed by a landslide, Sendiga said, adding that they did not know the whereabouts of people from 28 households.
Television images showed streets turned into rivers of mud carrying debris past flooded houses.
Climate change is causing more intense and more frequent extreme weather events, according to climate scientists.
The flooding comes on the back of the worst drought to hit the region in 40 years. Dry soils are less able to absorb water, increasing the risk of flash flooding.
In neighbouring Kenya, where floods have so far killed at least 142 people, the banks of the Voi River in the country's south burst on Monday, causing floods in villages in nearby Voi town, the Kenya Red Cross said on X, adding that its personnel were helping to rescue those who were stranded.
(Reporting by Nuzulack Dausen; Writing by Hereward Holland; Editing by George Obulutsa, Christopher Cushing, Nellie Peyton and Sharon Singleton)