Confirming the crash, Kericho Police Commandant James Mugera said among those who lost their lives were 31 males, 12 women and seven children.
"It is unfortunate that we have lost 51 people", Kenya's police chief Joseph Boinnet said.
The 67-seater bus was headed to Kisumu from Nairobi when it reportedly veered off the road and rolled over at Fort Tenan black spot.
Fort Ternan is a small town in Kericho County, just 50 kilometres east of Kisumu.More news: New NES Games Now Available
Police estimate that the Western Express bus had 52 occupants.
Emergency personnel and security forces inspect the wreckage of a bus at the site of an accident in Kericho, western Kenya, on 10 October 2018.
Footage from the scene showed the faded red bus lying on its side, the seats and mangled bits of metal exposed to the air with the torn-off roof lying at a distance.More news: Google unveils Home Hub
President Uhuru Kenyatta said authorities were investigating what he called a catastrophic incident.
"I would like to remind drivers to always exercise caution to avoid such catastrophic incident", he said on Twitter.
Kenya has struggled to reduce the rising number of road accidents as more people acquire vehicles in the country's growing middle class.
Last December, some 36 people died in a head-on collision between a lorry and a Nairobi-bound bus on a road near Migaa in Kenya.More news: Kevin Tway Wins First PGA Tour Event
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