The bus, traveling from Meru town to the coastal city of Mombasa, plunged into the Nithi River about 40 meters below along the Meru-Nairobi highway at around 6:40 p.m. (1540 GMT), Eastern Regional Police Commander Rono Bunei said on Monday, Xinhua reported.
Bunei said the bus must have developed brake failure because it was at a very high speed when the accident happened.
The wreckage of the bus could be seen strewn on the hillside near the black spot.
Alex Mugambi, Tharaka Nithi County Rescue team manager, said the death toll may rise.
The accident is among a series of deadly crashes in the country. On July 8, more than 20 passengers were killed in an accident along the Nairobi-Mombasa highway.