The walls of the Patel dam, situated on top of a hill in Nakuru county, 190 km (120 miles) northwest of Nairobi, gave way late on Wednesday.
According to Nakuru Governor, Lee Kinyanjui the water from the dam has caused massive destruction of both property and life.
"We found 11 of the bodies covered with mud at a coffee plantation and these are people who may have been escaping but could not make it due to the force and speed of the water from the flooded dam", he said.
Preliminary reports indicate that at least 27 people have been killed, and over 2,000 rendered homeless.
The extent of the damage is yet to be ascertained, he said in a statement.
Police confirm that three more bodies recovered, bringing the death toll to 34.
A search and rescue operation led by police was set up and includes officers from the National Youth Service (NYS) as well as members of the public.
A disaster management team from the Nakuru County Government is also evacuating survivors to the Bahati Sub County and Nakuru Level Five hospitals.
Officials said the dam water and mud spilt out of the reservoir and submerged homes, extending to a radius of almost two kilometers (more than a mile) Interior Cabinet Secretary Fred Matiangi was set to visit the site on Thursday. "Looking at families being displaced, children, mothers, the elderly being swept away by floods, it's traumatizing".
The disaster comes after weeks of heavy rain.
The unusually heavy rains began in March and have so far killed at least 132 people.