The spokesman, Gerald Jimenez, said six critically injured people were taken to local hospitals.
The number of injured was not yet clear, nor was the nationality of those aboard the bus that ran off a mountain road north of the capital, San Jose.
Fire department spokesman Josue Lara said rescue units from the Red Cross and fire department were at the scene, as were two helicopters from the government security service.
He said the bus fell about 15 meters down the slope and came to rest upside down. He said officials feared some passengers could still be trapped.