Speaking in Denver, Mederos confirmed that midfielder Yasmani Lopez had left the squad after the Cubans were thrashed 7-0 by Mexico in their opening game of the tournament in Pasadena, California on Saturday.
"Regarding the case of Yasmani, it is a decision of him," Mederos said.
"None of the rest of the delegation had anything to do with it, it is a decision of him. He took it and made it," Mederos told a press conference.
Cuba face Martinique in Denver on Wednesday in their second game of the tournament.
Lopez, 31, is one of Cuba's most experienced players, making his debut in a Gold Cup clash against Belize in 2013.
The midfielder has been capped 28 times, scoring a single goal and has participated in five Gold Cup games.
Athletes from communist Cuba participating in sports events in the United States and Canada have a long history of defecting.
In 2015, several members of Cuba's Gold Cup squad defected during the tournament, despite thawing relations between the then administration of President Barack Obama and Havana.