Flum clashed with team mate Slobodan Medojevic, who was also slightly injured, and both players fell to the ground with Flum clearly in severe pain.
The 27-year-old former Germany youth international received initial treatment on the pitch before being flown to hospital.
"A serious knee injury for Johannes Flum. He is on his way to hospital," Frankfurt said on Twitter. Medojevic also injured his knee and underwent treatment at the training centre.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
The injuries could not have come at a worse time for Eintracht, who have won just once in their last 10 league games.
Lying 13th in the Bundesliga, they take on promoted Darmstadt 98 on Sunday.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
