"A village near that dam has been evacuated", Chimwanga said in a statement.
At the scene of the incident is a search and rescue operation.
The government said on Wednesday the rain had killed 132 people and displaced 222,456 in 32 counties since March.
Nakuru East Deputy County Commissioner Omar Salat assured the victims that the government would help them find temporary shelter and provide relief food. He said that it seemed like they had been fleeing but that they could not make it due to the speed and force of the water.
Water burst through the banks of the Patel Dam in Solai, Nakuru County, on Wednesday night, sweeping away hundreds of homes, including those on the expansive Nyakinyua estate that borders the reservoir. Two schools are among the hundreds of buildings destroyed by the flood.
An emergency response team from the Kenya Power and Electricity Company (KPLC) had to be called in to disconnect wires after several poles fell into the water.More news: Marion County Sheriff's deputy saves baby's life in Ocala
Survivor Ngugi Njoroge said he and his family had been having dinner when there was a "loud explosion of water that washed away our home".
In 2015, one of the dams burst its banks but no fatalities were reported. "The extent of the damage has yet to be ascertained", Lee Kinyajui, the governor of Nakuru, said in a statement.
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.
"We have recovered 38 bodies and many people are missing".
In Solai, Veronica Wanjiku Ngigi, 67, said she was at home brewing tea with her son at around 8pm local time when his wife rushed in to say the dam had burst and they needed to get to higher ground immediately.