President Laura Chinchilla, who supports the measure, is expected to sign it into law in the next days.
The ban, which does not affect fishing for sport, does allow researchers to hunt for scientific purposes.
Hunters violating the ban would have to pay a fine of up to $3,000.
Costa Rica supports an enormous variety of fauna, and is one of the countries with the highest density of biodiversity in the world.
Wildlife in Costa Rica include jaguars, armadillos, deer, sloths and several species of monkeys, as well as a variety of birds, amphibians and reptiles.
Some two million people visit Costa Rica each year -- a $2 billion business -- and the country's natural reserves and variety of species are a great attraction.