Local media reports that the fight erupted after a Chechen man asked a group of around 15 Turkish men to be quiet. The men were socialising at an Internet cafe near to Knöllgasse and Quellenstraße, in the 10th district.
The fight quickly moved outside to the street. At least 20 people were involved in the brawl and one Chechen man was reportedly armed with a knife.
In the course of the fight a Serbian man fell into the path of an oncoming tram, badly injuring both of his legs.
Police are investigating whether he was pushed or tripped. It's not clear whether he was a bystander or was involved in the brawl. He was taken to hospital for emergency surgery.
The other men were able to flee the scene and police have not confirmed whether any arrests were subsequently made.