The Colombia star was taken off in the second half of Tuesday's 3-0 Audi Cup loss to Liverpool after complaining of discomfort and was sent for further tests on the problem.
The Bundesliga champions have since revealed that he is facing a spell on the sidelines after muscle damage was detected.
"Bayern will have to do without new signing James Rodriguez over the coming weeks," the club said in a statement.
"As detailed checks by the Bayern medical department showed, the Colombian suffered a muscle injury in his right thigh in the 3-0 loss against Liverpool in the semi-final of the Audi Cup."
Bayern added that midfielder Thiago will certainly miss the DFL-Supercup clash with Borussia Dortmund on Saturday after sustaining an abdominal injury.
The knock picked up by David Alaba is not such a concern, though, although the Austria star will need to train away from the team over the coming days.