The Pirai river flows through Bolivia's most populous city, Santa Cruz, which is also the country's economic capital.
The worst-affected areas were the districts of El Torno to the southwest of the city and Colpa Belgica in the northwest, deputy minister for civil defense Alfredo Troche told local radio.
Families in El Torno climbed onto the roofs of their homes or trees to escape torrents of muddy water which poured through the streets, coating everything in mud.
Helicopters were dispatched to rescue them.
A bridge over the river collapsed in the floods.
"My son ended up sleeping on the roof and saved some people, including a man with a disabled leg," Elia Castro Suarez, a teacher in El Torno, told AFP on Sunday.
Vice President Edmand Lara said some families had lost all the animals they use for agriculture, as well as their personal belongings.
Over the weekend, President Rodrigo Paz convened a crisis meeting of key ministers and senior police and military officials to discuss the situation.
He warned that Bolivia was experiencing a "very complex moment" due to the convergence of the La Nina and El Nino climate patterns.
"In these first few days of the rainy season, we have broken all the reported records of the last 100 years," Paz said.
El Nino warms the sea surface in the Pacific Ocean, leading to hotter weather globally.
La Nina has the opposite effect. It cools surface temperatures in the central and eastern equatorial Pacific Ocean.
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