Vehicles were buried in drifts of hail stones
Fire Department chief Rolando Buscara said another 120 had been injured. Hospital officials expect casualties to rise.
An unknown number of people are feared trapped by mud and water in a subway beneath La Paz's main street, El Prado, after the Choqueapu river burst its banks.
Streets impassable
A large government building near the centre of the city is also in danger of collapse, reports say.
A spokesman for the mayor of La Paz said the hail storm, which struck early on Tuesday evening, was the heaviest "the city has ever seen".
According to the BBC's Andrew Enever in La Paz the city's steep hills funnelled water down streets, making them impassable within minutes and causing huge flood damage.
In one street vehicles were covered in hail stones to a depth of 1.5 metres (five feet) and a nearby underground car park was filled to the ceiling with ice and debris.
Rescue efforts
Some people have been brought out of the El Prado subway alive.
But Dr Carlos Tamaya, a Red Cross official at the scene, said attempts to rescue those trapped were being hampered by mud slides and fast moving water.
He said a subway attendant had been killed trying to shut the subway doors to keep the water at bay.
Last year heavy rains caused mudslides and significant casualties in La Paz and there are fears that the same might occur after these storms - local people are being advised to stay in their homes.