The landslide hit West Pokot County on Saturday following a night of rainfalls.
Bodies of the 15 victims have been recovered, while the search for the other 22 is still underway, the Citizen TV channel reported, citing West Pokot County Commissioner Apollo Okello.
The Kenyan government reportedly announced that military and police helicopters had been dispatched to the area for search and rescue operations but bad weather hampers the efforts.
Local authorities, in turn, told the broadcaster that there were other people remaining unaccounted for.