He will have an operation on Friday after ligament damage was discovered, even though club doctor Wolf Schwietzer was able to put the shoulder back into place following Flum's substitution during a 2-0 win over Mainz.
"Of course this is very bitter for us because the team's been in particularly good shape of late and Johannes is an important part of it," said Frankfurt director of sport Bruno Hubner.
"We're going to miss him a lot and have got to find a way of covering for him."
In leaving the field on Saturday, Flum may also have played his last game for Frankfurt.
His future has been cast in doubt following coach Armin Veh's announcement that he will be leaving in the summer.
Flum joined the club from Freiburg last summer because he was convinced to do so by Veh.