The Patel dam, located on private farmland, and reportedly used for irrigation and fish farming, broke its walls and swept away hundreds of homes downstream.
"We have 41 people dead from this tragedy", Kibunjah said, adding 20 of them were children.
The town and its environs are home to commercial farms that supply markets in Europe, producing everything from cut flowers to beans, fruits, and vegetables.
Up to 40 people were rescued from under the mud - many more are feared trapped - and taken to hospital on Thursday morning by the Kenya Red Cross and Nakuru County disaster management teams.
Authorities are now responding to the disaster area in Solai, where homes over a radius of almost 1.2 miles have completely been submerged.
Governor Kinyanjui said 450 homes had been hit by the floodwaters and safety engineers had been sent to inspect three other dams to check for cracks or breaches.
"There are two other dams which are leaking", one resident, Stephen Nganga, said.
The bursting of the Patel Dam in Solai, Nakuru County, on Wednesday night was the deadliest single incident yet in the seasonal rains that have killed more than 170 people in Kenya since March.
Koigi said that although they have been inconvenienced by the dams, residents were grateful to the the farmer because of the benefits to them from his community service.
Interior Cabinet Secretary Fred Matiang'i and Inspector General of Police Joseph Boinnet also visited the scene to access the damage.
The bodies of two women were found several km (miles) away as excavators and rescue workers armed with shovels picked through rubble and mud searching for survivors and victims.
In April 2016 a residential building in the capital, Nairobi, collapsed during rains, killing 52 people.