Police fear the death toll may rise, with the possibility of passengers trapped in the wreckage.
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.
The bus belonged to Western Cross Express but the operational name is Home Boyz.
The bus was going from Nairobi to Kakamega with 52 passengers on board.
A dawn accident has claimed 51 lives along Londiani-Muhoroni road, within Kericho County.
The wrecked bus is seen at the scene of a bus crash near Kericho in western Kenya Wednesday, Oct. 10, 2018.
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The Daily Nation newspaper quoted Traffic Commandant Samwel Kimaru as saying that 2,345 people have died in road crashes across Kenya in the past 10 months, an eight percent rise compared to previous year.
"The roof of the bus was ripped off", a local official said.
"I would like to remind drivers to always exercise caution to avoid such catastrophic incident", he said on Twitter.
"My heartfelt condolences to the families of fellow Kenyans who lost their lives in a tragic road accident at Fort Ternan in Kericho County this morning and wish those in hospital quick recovery", Uhuru said.
Kenya has struggled to reduce the rising number of road accidents as more people in the growing middle class acquire vehicles.
In 2016, more than 40 people died when an out-of-control fuel tanker rammed into vehicles and then exploded on a busy stretch of highway.