NAIROBI, Kenya—Ethiopia said it plans to sell stakes in some of the country’s most-prized assets after decades of state control, including telecommunications company Ethio Telecom and booming Ethiopian Airlines, liberalizing one of the world’s fastest-growing economies.

If implemented, the move, announced late Tuesday by the Ethiopian People’s Revolutionary Democratic Front, will present one of the biggest business opportunities in Africa to foreign and domestic private investors, but also one of the most complex.

Ethiopia’s...