The Colombia Football Federation announced that the 28-year-old complained of discomfort after twisting his left knee near the end of Thursday's training session.
"The Colombian National Team reports, that during the training this Thursday, in an accidental move, James Rodriguez complained of a discomfort in his left knee," the governing body said in a statement.
"For now and as a precaution, the player James Rodriguez is ruled out for the match against Peru.
"In the next few hours, a detailed imaging study will be carried out to confirm the definitive diagnosis, which will be shared with his club."
James has made just nine appearances for Real this season and has scored one goal.