Ten people died in the south-eastern coastal region, and two refugees in Kenya's north-eastern Dadaab camps drowned.
"The situation has been difficult for several days now," Tourism Minister Morris Dzoro, whose constituency is in the affected coastal area, told Reuters.
Many students sitting their national high school exams have been cut off from their schools and examination centres because of the floods.
"The floods are yet to subside and life is difficult in the affected areas. We are using one chopper to transport food, examinations and students," Dzoro said.
Fearing landslides, many in Kwale district of the coastal region have moved to higher ground, while major roads have been blocked due to weeks of downpour in the region's Kilifi district.
"We have 60,000 people stranded on higher ground and (major) roads are still inaccessible," Coast Provincial Commissioner, Ernest Munyi, told Reuters.
"We are appealing for help in terms of food, medical attention and transportation. The government continues to mobilise available resources to get help to the affected," he added.
The UN refugee agency UNHCR said a pregnant woman and a child had died in Dadaab, which houses more than 150,000 mainly Somali refugees in three camps, and more than 12,000 people had lost their shelters.
"Two deaths by drowning were reported and considerable damage caused, especially in shelter, where many structures have collapsed or have been washed away," Eddie Gedalof, UNHCR's acting representative in Kenya, said in a statement.
Heavy rains have been pounding the region, bringing misery and death to parts of Somalia, Ethiopia, Sudan and Eritrea.

Copyright Reuters, 2006