The downpour on Saturday night swept large tree trunks and debris from surrounding mountains into the community of Tejerias, 70 kilometres southwest of Caracas, damaging businesses and farmland, Venezuela Vice-President Delcy Rodriguez said.
Pumps used to power the community's drinking water system were carried away in the flood, she said in a televised address on Sunday.
Rodriguez said the priority was to find people still trapped under mud and rocks throughout the town, while military and rescue personnel also searched the riverbanks for survivors.
"We have lost boys, girls," the vice president said from a flooded street in Tejerias.
"What has happened in the town of Tejerias is a tragedy."
The state television channel aired images of muddy streets filled with tangled tree branches and large rocks.
One of the flooded rivers, the El Pato, swept away several houses, shops and a slaughterhouse, according to search and rescue authorities.
Carlos Perez, deputy minister for the country's civil protection system, said in a Sunday tweet that a thousand rescuers were looking for victims in the area.
The downpour also caused landslides in three other central states on Sunday morning, Rodriguez said, but claimed no victims.
The deaths bring the total killed in recent weeks to at least 40 due to heavy rain caused by the La Nina weather pattern. Venezuela has faced flooding and landslides.
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