The floodwaters swept away powerlines, homes and buildings, including a primary school, a Reuters photographer on the scene said.
Regional criminal investigation commander Gideon Kibunja who confirmed the death toll said several people are still not accounted for after Nakuru's Patel Dam broke its banks.
"We have adjourned search and recovery operation until tomorrow (Friday) morning. My neighbor was killed when the water smashed through the wall of his house", Veronica Wanjiku Ngigi told Reuters.
Officials said about 40 people had been rescued and taken to hospitals, and rescue crews continued searching Thursday for more people who could be trapped.
At least 132 people have died and more than 225,000 displaced, from floods caused by seasonal rains since March, according to a government statement.
Heavy rain has battered Kenya and other East African nations over the past two months. The disaster comes after three failed rainy seasons inflicted a crippling drought that sent food prices soaring and left more than three million people requiring food aid.
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The dam burst the night of may 9 near the town of Solai.
Esipisu said: "We are saddened by the loss of lives and property occasioned by the bursting of Patel dam in Solai, Subukia".
"There is another dam which is also overflowing which is looking risky", she said.
Interior Cabinet Secretary Fred Matiangi and Inspector General of Police Joseph Boinnet are also at the scene.
Governor Lee Kinyanjui said Nakuru County was working closely with KRCS as well as the security agencies to coordinate rescue missions.
As a result of the dam in Kenya, killing at least 20 people, and about forty were injured varying degrees of severity.
The floods have also destroyed road networks in some parts of the country.