The aircraft, a single-propellor Cessna 208 Caravan, came down in a mountainous area near the Pacific coastal beach town of Punta Islita in the country's Guanacaste peninsula, the spokesman, Carlos Hidalgo, said on his Facebook page.
"It is a private plane with 10 foreign passengers and two local crew members," a separate security ministry statement said.
Hidalgo published images of the crash site, showing flaming wreckage strewn across the terrain.
The US embassy said it was aware of the crash and was "trying to confirm if any US citizens are on board.