Nicaraguan government spokeswoman and First Lady Rosario Murillo said that "of the 32 passengers, 13 lost their lives, all of them are Costa Rican."
She said the other passengers survived and were taken to nearby Big Corn Island.
The Corn Islands, made up of Big Corn Island and Little Corn Island, are located around 70 kilometers (45 miles) off Nicaragua's mainland. Although remote, they are becoming increasingly popular with tourists.
Costa Rica's foreign ministry identified nine of its citizens who drowned, two of whom were US residents.
It said in a statement there had been 25 Costa Ricans, four US citizens and three Nicaraguans on the small vessel, which got into trouble "after strong winds... on Little Corn Island."
Media reports said the captain, who was also owns the vessel, was arrested after being rescued, as authorities began an investigation.
