Riot police had to move in to separate the supporters in Eugendorf, to the north of the Austrian city of Salzburg, with 25 arrests being made.
Fans of both clubs were arrested after they confronted each other on the pitch after the final whistle.
Footage of the fighting has been posted online and can be viewed, courtesy of Daniel Brambock, here.
There was trouble before the match even started, however, with four fans of the Bundesliga club arrested as some stormed the entrance to the stadium.
Sky Austria reported that one Leeds fan threw a bench at the police, with supporters also lighting flares during the game.
It was also reported that police had to use pepper spray and that more trouble took place in Eugendorf city centre.
The violence resulted in injuries to police officers, private security guards and supporters.
Leeds have been contacted for comment.