The 25-year-old Spain international has added to the club's midfield injury crisis, following recent injuries to Thiago Alcantara, Bastian Schweinsteiger and Mario Gotze
Bayern's record signing picked up the injury against Ecuador for Spain in a friendly last month, while he also strained knee ligaments in Bayern's Super Cup victory over Chelsea on Friday.
Despite scoring a late equaliser against Jose Mourinho's side, the 25-year-old stated after the game that he struggled for much of the contest.
"I had no problems for 20, 30 minutes, but then it started to hurt again," he said.
Meanwhile, Bayern sporting director Matthias Sammer has complained to the Spanish FA following Martinez's injury in South America, calling the trip "an effrontery and an imposition for the players".
Martinez signed from Athletic Bilbao in August 2012 for €40 million (£33m), and was a key man in Bayern's historic treble-winning season.