The Colombian international sustained the injury while training last Thursday with his national team ahead of its international friendly against Peru.
James returned to Madrid on Monday and underwent tests that revealed "a sprain to the internal ligament of his left knee."
Madrid said in a statement that James' recovery "will continue to be assessed" although it is expected that the player will be ruled out of action for at least three weeks.
The former Bayern Munich star, who has not played for Madrid since Oct. 22 because of a muscular injury, was nevertheless called up to the national team for the first time since this summer's Copa America.
James has scored one goal in nine appearances for Los Blancos this season and is expected to miss his team's next five games.
The 28-year-old could return to action when Madrid face Valencia in La Liga on Dec. 15 with the Clasico at Barcelona three days later.