Among the passengers were six members of parliament.
Officials said the Chinese-built Kenyan Air Force Harbin Y-12 twin-engine turboprop went down at around 10am (0700 GMT) and burst into flames near Marsabit National Park, about 430km northeast of Nairobi.
Mutea Iringo, Marsabit district commissioner, said the plane had crashed into a hill in heavy fog as it approached the airstrip outside town.
"They lost direction of the airstrip because of foggy weather and then crash landed on a hill about three kilometres from Marsabit town," he told AFP.
"After it crashed, it burst into flames and the fire was so fierce that some of the bodies were burnt beyond recognition."
The passengers, a group of MPs and local officials, were on their way to the northeastern town of Marsabit on Monday to mediate between warring communities in the area, where conflict over pasture and water is common.
By afternoon, emergency teams had put out the flames in the wreck of the aircraft, split into pieces with only its tail left intact.
The crash occurred northeast of
Nairobi, the capital
Francis ole Kaparo, the National Assembly speaker, said: "It appears that we have lost about six members of parliament."
Colleagues named some of the members of parliament as Bonaya Godana, Titus Ngoyoni, Abdi Tari Sasura and Guracha Galgallo.
Four people were pulled from the wreckage alive, witnesses said.
Mwai Kibaki, the president, expressed "shock and disbelief" at the accident.
It was Kenya's worst air accident since a light aircraft crashed into Mount Kenya in July 2003, killing 14 people, including 12 members of an American family.