Most of those on board the flight were foreign tourists, according to the country's security ministry.
The ministry also said later that 10 foreigners were passengers aboard the plane, which was flown by two Costa Rican pilots.
The reason for the crash is not yet known.
The country's Ministry of Public Security said in a statement that the aircraft went down in Guanacaste, a province in the country's northwestern corner popular with worldwide tourists.
Hidalgo published images of the crash site, showing flaming wreckage strewn across the terrain.
One of the victims was the cousin of Costa Rican ex-President Laura Chinchilla, the former leader said on her Twitter account.
"There are no people alive", security minister Gustavo Mata said.
The plane, operated by Nature Air, had taken off nearby and was heading to Juan Santamaria International Airport when it crashed in a wooded area around 12:16pm local time.