Riot police moved into separate fighting fans at full-time after United’s game in Austria descended into violence.
Around 100 Frankfurt supporters - some of them wearing balaclavas - confronted a contingent of Leeds fans as supporters spilled onto the pitch at the end of United’s 2-1 defeat.
An officer with the local police force said around 20 arrests had been made, including supporters of both clubs.
One Leeds fan and one officer needed medical treatment, the officer said.
The pre-season friendly in Eugendorf - a town to the north of the Austrian city of Salzburg - drew a crowd of several hundred, the majority of them Leeds fans.
A group of Frankfurt supporters were held outside the ground shortly before kick-off but allowed into the 2000-capacity arena as the game kicked off.
The match passed off without incident until the final whistle when police with batons and dogs fought to form a cordon on the pitch.
A Leeds fan was treated by paramedics for a facial injury in a nearby car park.
Neil Slinn, 53, from Garforth was among the fans hurt in the violence
He said: “A few of us went over to applaud the Frankfurt fans. I was going to shake their hands. Then their ultras jumped over the (advertising) boards and started attacking us. Some were wearing balaclavas and we were outnumbered.”
United are midway through their pre-season tour of Austria and are training in the village of Kossen, 50 miles to the west of Salzburg.
Head coach Uwe Rosler and his players had left the field by the time the fighting broke out and were not hurt.