Mario Berrios, the Nicaraguan navy's commander for the southern Caribbean region, said the dead were all Costa Rican nationals who were traveling aboard the Reina del Caribe, Spanish for "Caribbean Queen."
The vessel went down amid rain and strong winds as it was ferrying between the Corn Islands, a popular tourist destination. Berrios said that of the 32 passengers on the boat, 25 were Costa Ricans, four were Americans and three were Nicaraguans.
He added that most of the 13 dead were women. The other 19 passengers were rescued.
"This is a great tragedy, truly painful, because they were our Costa Rican, Central American brothers and sisters who were vacationing in the waters of the Nicaraguan Caribbean," government spokeswoman Rosario Murillo told the official media portal El 19 Digital.
Berrios said the boat's captain and owner was detained because the vessel was not supposed to be sailing during the inclement weather that has been lashing the region for several days.
"There was a warning that the weather conditions would be bad, but it appears that was ignored and this tragedy happened," Berrios said.
Authorities had suspended boat launches in the area due to winds reaching 25 to 30 knots (29 to 35 mph).
Nicaraguan authorities were working with their Costa Rican counterparts to repatriate the bodies Sunday.
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