The plane, a twin-turboprop Beechcraft 300, declared an emergency two hours into its flight from the southern city of Punta Arenas to Santiago, said civil aviation authorities.
The head of the operating company Inaer, which conducts medical evacuations, said the plane was carrying two crew members and five passengers.
Punta Arenas is one of the southernmost cities in the country, some 3,000 kilometers (1,860 miles) from the Chilean capital.