"It is a horrible scene. Bodies are strewn all over," traffic police official Samuel Kimaru said by telephone from the scene near the town of Narok.
The bus was travelling from Nairobi to Homa Bay on the banks of Lake Victoria when it flew off the road, rolled over and plunged down a hill.
"It is difficult to tell exactly what happened but all indications point to speeding and possibly overloading," he said. "It is quite disturbing."
Police also told the Standard newspaper that the driver may have fallen asleep.
The Red Cross said the accident occurred shortly after 2:00 am (2300 GMT Wednesday) some 160 kilometres (100 miles) west of the capital.
