The paper reported that the dam burst left over 500 families left homeless and affected around 2,500 residents.
The breach happened on farmland near the town of Solai, 190km (120 miles) north-west of the capital, Nairobi. Local officials say neither the extent of the damage nor the death toll are yet clear.
The mega dam is one of the three water reservoirs owned by a large-scale irrigation farmer, Mr Mansukul Patel, who was not around at the time of the tragedy.
The Kenya Red Cross Society (KRCS) reported that thirty-nine people had been rescued in a joint operation with the county government and were admitted to Bahati sub-county and Nakuru County Referral Hospital.
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The St. John Ambulance service said at least 21 people had been killed downstream of the dam.
He said 36 people had been hospitalised.
At least 225,436 people have been displaced from their homes, according to a government statement.
Among villages affected are those in the farmlands of Nyakinyua, Endao, and Arutani where hundreds of people were displaced. However, the torrential rains and floods have made it hard to reach those most in need. Military helicopters and personnel have for the past week been deployed to rescue people marooned by the flooding.
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Kenya, like other countries in East Africa, has experienced heavy rain over the past two months. Many of those affected were already greatly in need of assistance following the 2017 drought.
A billion Kenyan shillings is worth roughly £7.3million.
A young woman walks in floodwaters after a heavy rainy season downpour at the Dadaab refugee complex, in the north-east of Kenya, on April 17, 2018.
The extreme weather comes at a time when the country is also trying to tackle a cholera outbreak as well as an epidemic of the mosquito-linked chikungunya virus. On Wednesday, the United Nations office for the co-ordination of humanitarian affairs reported a death toll of 118, up from 100 on May 4.
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