The flooding struck at about 9 p.m. Wednesday in and around Solai, a cluster of villages northwest of Nairobi.
Regional police chief Gideon Kibunjah confirmed the death toll has risen overnight to 38 and the disaster left 40 people needing hospital treatment.
He said 36 people had been hospitalized. The deaths from the dam burst raise the death toll to almost 170 people.
The capital, Nairobi, and the Rift Valley in the country's west are among areas where rain is expected to continue in the seven days to May 14, the Kenya meteorological department said on its website on Monday. The floods hit as the East African nation was recovering from a severe drought that affected half of the country.
At least 32 people have died and many others are missing.
Officials said floodwaters swept away power lines, homes, buildings and a school.
Arriving at the scene, Interior Minister Fred Matiangi pledged central government assistance to those affected.
At least 200 Kenya Defence Forces soldiers arrived in choppers to help Red Cross and the county.
"There should be no confusion and no wasting time", he said, while directing thorough logistical, health and other operations.
He said that the national government will work closely with the county government in order to ensure food, medical care and beddings are supplied to the victims.
Originally reported eight fatalities, however, according to updated information, the tragedy killed at least 20 people. "I'm so confused. I hope they are alive", she said.
Nearly an entire village was swept away by silt and water from the burst dam, said Gideon Kibunja, the county police chief in charge of criminal investigations. The search for victims on Thursday afternoon by heavy rains.