"We know there are eight dancers who decided to leave the company and not return to Cuba," Jorge Luis Sanchez, father of one of the performers, told local media in Puerto Rico.
"Of those, some went on to Miami and others are in Puerto Rico, waiting to travel on," he said.
Puerto Rico is a mostly Spanish-speaking US Caribbean commonwealth. Since it is legally part of the United States, some dancers traveled on to Miami easily by air.
The number of dancers who defected after a performance at San Juan's Centro de Bellas Artes could not immediately be confirmed.
The Cuban delegation that traveled to San Juan included more than 50 people, including the ballet company's famous longtime director Alicia Alonso, 92.
The visually impaired prima ballerina returned to Cuba from New York just after Fidel Castro's 1959 revolution.
The successful company she founded was for decades a centerpiece of the Cold War cultural offerings of the only Communist country in the Americas.