The Croatian had already been ruled out of his country's winner-takes-all game against England on Sunday in the new competition and was sent back to Barcelona, where he underwent tests on Saturday.
Barca's medical report did not state how long the 30-year-old midfielder would be out for, although Spanish newspaper Mundo Deportivo said he was expected to be sidelined for two to three weeks.
Rakitic was already suspended for next Saturday's clash between the Liga leaders and third-placed Atletico Madrid, who are a point behind, after being sent off against Real Betis last week.
He is now certain to miss the Champions League trip to PSV Eindhoven on Nov. 28 and a Liga game at home to Villarreal on Dec. 2.
(Reporting by Richard Martin; editing by Ken Ferris)
