The two men who drove the fleeing car have been arrested.
This is the first time capybaras, also called water pigs, have been seized in Costa Rica. The rodents are not naturally occurring in Costa Rica and it is illegal to possess, transport, or smuggle them.
The police's action was important and shows that the drug world is linked to the introduction of foreign species, says the country's security minister Mario Zamora.
Capybaras are the world's largest rodents and can weigh up to over 60 kilos. The Latin American animals, which have recently become increasingly popular on social media, live partly in water.