The Real Madrid midfielder, 28, will miss the clash in Florida after hurting his left knee, the Colombian Football Federation (FCF) said in a statement on Thursday.
James complained of "discomfort" in his left knee during training, leading to the FCF ruling him out of the Peru fixture.
"The player was evaluated by the medical body and his first diagnosis is reserved," the statement said.
"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."
Colombia are winless in their past five matches and will also face Ecuador on Tuesday.
James has made nine appearances for Madrid this season, scoring once.