An MRI scan at a Madrid clinic revealed that Costa had picked up a torn right thigh muscle during Atletico’s 1-1 away draw against Villareal on Sunday, the club said in an online statement.
The injury delays Costa’s long-awaited and controversial start for Vicente del Bosque’s Spain squad.
“This injury will prevent him from accepting Vicente del Bosque’s call-up for the Spanish national team for the games against Guinea and South Africa, for which he had been named,” Atletico Madrid said.
“The striker will be on a sporting rest undergoing physiotherapy,” the club said.
Costa, who has also acquired Spanish nationality, was called up last week for the friendly matches against Equatorial Guinea and South Africa later this month.
The Atletico Madrid man declared his intention to play for Spain, for whom he qualifies on residency grounds, and rejected a call-up from Brazil boss Luiz Felipe Scolari last month.