Strong winds on Saturday caused the boat to capsize amid poor weather conditions between Corn Island and Little Corn Island, two islands about 70km off Nicaragua's eastern coast.
"We are talking about 21 survivors and 13 dead, four of whose bodies have not yet been recovered," said presidential spokeswoman Rosario Murillo said.
Among the 21 survivors are 13 Costa Ricans, two Britons, two Americans, three Nicaraguans and one Brazilian.
The ship's captain, Hilario Blandon, and his assistants Carlos Prack and Shura Bonlye Welcome were rescued.
The bodies of the victims will be transported by air from the Caribbean coast of Nicaragua to the Pacific, where they will be medically examined before being repatriated to Costa Rica, Murillo said.
Authorities are detaining Blandon, the ship's captain, who allegedly sailed without authorisation under adverse weather conditions.
The Naval Force of Nicaragua and the National Port Company have redoubled their security systems to prevent other small boats from setting sail without permission.
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