The bus, with about 50 passengers, was heading to the capital, Nairobi, from northern Wajir county, police said.
The driver had attempted to cross a flooded section of the road when it happened. The bus then became stuck in some mud surrounded by raging waters.
Some of the passengers were rescued from the roof of the vehicle.
The Kenya Red Cross said it was a “challenging rescue operation” to save the lives of who were “marooned by raging waters” in the Lager Areli area near Tulla village in Tana River county.
The incident occurred in the early hours of Tuesday following ongoing rains that have left the Garissa-Nairobi Highway heavily flooded.
Videos shared on social media showed the bus, owned by Umma Express, becoming submerged in the flood water.
Ali Ndiema, the regional police chief, told Kenya’s Nation news website that the driver had “risked the lives of more than 50 people”, adding that this was a punishable offence.
The Kenya Red Cross said it had collaborated with members of the nearby community to reach the passengers.
Two of its boats are continuing to rescue other commuters stranded as the road remains impassable.