Police in Bujumbura said the toll was the highest in living memory from a disaster caused by freak weather, with more than 100 people also injured.
"The rain that fell in torrents overnight on the capital caused a disaster," Security Minister Gabriel Nizigama told reporters.
"We have already found the bodies of 51 people killed when their houses collapsed or were swept away."
Nizigama said burials of the victims would begin today because there was not enough space for their bodies in the capital's mortuaries.
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An AFP journalist saw 27 bodies covered in white sheeting at the police station.
Police said several hundred homes were destroyed and more than 100 people injured in Bujumbura, which lies on the northeastern shore of Lake Tanganyika.
Houses in the poorer parts of town are often built from mud bricks, which offer no resistance to torrents of water and mud.
Nizigama, touring the disaster zone with other ministers, promised food aid to those who lost their homes and said the government would bear the cost of burying relatives and would provide new housing.
The road leading out of the capital to neighbouring Rwanda was blocked because of a landslide while a bridge was washed away on the road to the Democratic Republic of Congo.