The driver of the bus lost control of the vehicle and it rolled off the road, down a 16-foot drop and ended in the way of oncoming traffic, The Daily Telegraph reported.
"The driver lost control on the Makupa Causeway and veered off the road," said Joshua Wamukata, Traffic Commandant in Coast Province. The causeway links Mombasa island to the Kenyan mainland.
"The bus fell down a five meter [about 16 feet] drop and rolled over onto another road," he added. "It was very fortunate that there were no vehicles on the other road."
The bus was traveling from an Indian Ocean resort hotel to the city's Moi International Airport.
Mark Bizley, who was driving behind the bus at the time of the crash, said the bus lost control when a tanker in front of it began leaking water.
"We were behind the local coach company coach, which in turn was behind a truck carrying water that was leaking quite heavily onto the road. With all the water, the coach's wheels lost grip and started to snake. I could see the driver was really struggling to keep the vehicle straight and it just rolled down the embankment onto the other carriageway," Bizley said.
Police said one passenger was in a serious but stable condition. Several other passengers suffered minor injuries.
Police reports from the incident suggested that all the passengers were British.