"Kaka experienced discomfort during training. He had a scan and he will need to rest for 20 days," the Selecao's technical director Gilmar Rinaldi said on Wednesday, Xinhua news agency reported.
The 34-year-old Orlando City midfielder, who was last week called up to replace injured winger Douglas Costa, was ruled out of the tournament in the US with an unspecified muscle injury.
He will be replaced by 26-year-old Sao Paulo midfielder Paulo Henrique Ganso, who has not played for Brazil's national team since 2012.
Kaka, a member of Brazil's 2002 World Cup-winning team, is the fifth player to be omitted from Brazil's Copa America squad due to injury.
Others are winger Douglas Costa, goalkeeper Ederson, midfielder Rafinha and striker Ricardo Oliveira.
Brazil are also without their captain Neymar after his club Barcelona refused to release him for both the Copa America and the Olympic Games in August.
The Selecao will begin their Copa America campaign against Ecuador at the Rose Bowl in Pasadena on Saturday.