The state television of the Greater Antilles confirmed the information, the AFP agency reported.
Santa Cruz debuted in March in the Dominican Circuit Opening tournament and is currently second in the goal table with seven, only behind the Argentine Pablo Marisi (Pantoja), who is 12.
In addition to Santa Cruz, Andy Baquero, David Urgellés, Orlendiz Benítez and Alejandro Portal left the team after being defeated by Canada 6-0 on Saturday in Toronto, the television said as "unfortunate" the news.
Canadians and Cubans are part of Liga A. On Tuesday both teams meet again, but in Havana.
Santa Cruz, considered one of the best footballers on the island, and Baquero, both 25, integrated the Cuban Under-20 team that achieved the feat of qualifying for the Turkish World Championship in 2013, the only participation of the island in those you lead
For its part, Portal (23) is considered by experts as a midfield talent. Urgellés is 24 years old and Benítez 23.
With these five players there are already 44 players who have defected from the Cuban national team in different tournaments in the last 17 years, including four that did so last June in the Gold Cup.
Osvaldo Alonso, one of the first to defect in 2007, triumphs in the Minnesota United FC of the US Major League Soccer, while another Cuban, Jorge Luis Corrales, plays with the Chicago Fire, also of the MLS.