It destroyed everything in its path - including a primary school and power lines.
Ngugi Njoroge, one of dozens receiving treatment for his injuries, told reporters from his hospital bed he was separated from his family.
"I was with my parents and my younger brother," he said. "I don't know where they are. I was carried away by the water but I was lucky as I clung to a tree until the water subsided."
Nakuru county governor Lee Kinyanjui said there were 40 people had been reported missing and were yet to be found. Another 44 were confirmed to have died, he added
The dam, which is located on private farmland, and reportedly used for irrigation and fish farming, burst after heavy rains in the area, which continued into Thursday, making rescue efforts more difficult.
There are fears over other dams in the area, with Mr Kinyanjui warning at least one other local dam "will have to be discharged to avoid disaster".
Before Wednesday's disaster, 132 people had died countrywide as a result of heavy rains since March, according to official statistics.
More than 220,000 people have also had their homes destroyed.
The rains came after a severe drought which left millions of people in need of food aid in the region.