Onlookers screamed as the yellow school bus hired to take a church choir and other revellers to the ceremony in Kitui County keeled over and sank as the driver tried to navigate the surging waters.

Some aboard the stricken bus managed to escape before the bus was quickly submerged, and were helped to safety.

"We have this terrible, terrible accident that happened here this morning," Kitui governor Charity Ngilu told reporters.

"The bodies that have already been retrieved right now are over 23. We have more bodies in the bus," she said, adding that efforts to recover the corpses would resume on Sunday morning.

She said 12 people had been rescued, including four children.

It remains unclear how many passengers were aboard the bus when it tipped into the Enziu River, about 200 kilometres (125 miles) east of the capital Nairobi.

Witnesses said the driver had stopped to negotiate the river, and was close to the other side when the bus was swept beneath the churning currents.

Deputy President William Ruto was among those to extend his condolences, and also urged motorists to apply extra caution on the roads with many parts of Kenya experiencing heavy rain.