Diario Extra said the victim was bitten yesterday in the morning at the mouth of an estuary in Tamarindo, a town in northwestern Costa Rica that is favoured by surfers and eco-tourists.
The newspaper said the man, a 50-year-old from Arizona, suffered partial amputation of his right ankle and was also wounded in the neck.
Primero en Noticias reported that most of his calf muscle was stripped, and he was hospitalised to undergo reconstructive surgery.
The US Embassy in Costa Rica said in a statement that it was aware of reports that an American citizen had been attacked by a crocodile. It said consular officers help US citizens when they are injured overseas, but declined to comment further citing privacy considerations.