Local television channel KTN News reported that 20 bodies have been recovered so far.
The burst happened in Solai near the Rift Valley city of Nakuru, 120 miles northwest of the capital Nairobi, late on Wednesday.
The 9pm horror rendered over 300 families homeless and about 2,500 residents were affected.
"The water has caused huge destruction of both life and property". People were feared to be trapped in thick mud stretching over a mile.
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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.
In Solai, Veronica Wanjiku Ngigi, 67, said she was at home brewing tea with her son at around 8 p.m. when his wife rushed in to say the dam had burst and they needed to get to higher ground immediately.
Nakuru County Governor Lee Kinyanjui stated that his office will do its best to ensure those affected are taken to a safer place.
Police, Red Cross, NYS and the Nakuru County Government workers continue rescue operation.
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Residents leave after their houses were destroyed by floodwaters from Patel Dam in Solai Ward, Subukia.
"The extent of the damage has yet to be ascertained".
"The county has dispatched ambulances to the scene to aid in the evacuation of victims". So far over 300 homes are confirmed to have been affected.
The disaster comes after weeks of heavy rain.
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He said the county government will donate foodstuffs and other items to the displaced families on Thursday.