The accident happened on Wednesday morning in Samburu, about 350 kilometres from the capital, Nairobi, a person with knowledge of the matter told AFP.
"I can confirm that an accident has occurred and that there are no survivors," the source said.
It is unclear exactly how many people were on board. The Kenyan newspaper The Star reports that six tourists died, but there is no information on their identities.
The Star has spoken to witnesses who described black smoke and flames rising from the impact site at the foot of Mount Ololokwe.
Pictures in the newspaper show a completely destroyed wreck. Rescue personnel are reportedly at the scene and an investigation has been launched.
