Sane sustained the problem in the shock 4-1 away defeat to Hoffenheim in the Bundesliga.
He will subsequently be missing for the Klassiker contest against Dortmund, while David Alaba is a doubt and will be checked closer to kick-off due to a muscular injury.
Sane, who scored on his debut for the club against Schalke this month after signing from Manchester City, will also be out for Bayern's weekend league meeting with Hertha Berlin, their last game before the international break.
"David has muscular problems, so we have to wait and see how that develops," explained head coach Hansi Flick at his pre-match news conference.
"But Leroy is out - he has a capsule injury in his right knee and hopefully he will be back after the international break."
Dortmund beat Bayern 2-0 in the 2019 Supercup, with Flick's men, who had won it in the previous three years, at home for this meeting as they look to bounce back from the Hoffenheim loss.
"Dortmund have a fantastic, young side and they also have experience in their ranks," said Flick.
"They play attractive, offensive football, which I like. This will be a test against one of Germany's best. This game will help to develop us.
"My team's mentality is absolutely outstanding. Maybe one or two of them are slightly tired, but they always give 100 per cent on the pitch.
"That was also the case in Hoffenheim, but unfortunately, we didn't do some things that well that day."
With Sane injured, Champions League final hero Kingsley Coman is in contention to join Serge Gnabry and Thomas Muller in support of striker Robert Lewandowski.