In a statement, Cuba's interior ministry said that the speedboat's passengers opened fire on a coast guard vessel that approached them.
Six additional passengers were wounded in the incident, which took place near an island on Cuba's northern coast.
The identities of those on board the vessel or what it was doing in the area are unclear, with the Cuban government saying an investigation has been launched to "clarify" the event.
In statement posted on X, the ministry said the Florida-registered vessel - with the registration number FL7726SH - was detected near Cayo Falcones, in the country's central Villa Clara province on Wednesday morning.