The teenager, from Lower Austria, had to be treated in hospital for serious facial injuries including a fractured jaw.
Police spokesman Thomas Keiblinger said that four teenagers are being investigated on suspicion of violent assault, which took place near the Kagran U-Bahn station in Vienna's Donaustadt district.
The ringleaders are thought to be a 16-year-old Chechen boy and a 15-year-old Austrian girl who is in social care. The Chechen youth, who came to Austria as a refugee, went to a police station on Saturday to say that he had been involved in the assault - after seeing the reaction on Facebook and realising that his name and telephone number had been posted in the comments.
The video was shared on Facebook over the weekend and by Monday morning it already had 2.8 million views. The 15-year-old girl is slapped in the face by three girls, and doesn't attempt to defend herself. She remains calm, rearranges her hair, and doesn't shout for help.
Towards the end of the video the 16-year-old boy appears and hits her several times in the face - after which she is seen spitting out blood. The teenagers are heard encouraging each other to hit the girl harder and one of them suggests that she is being punished for taking off her headscarf (although none of the other girls are wearing headscarves).
The video, which is three minutes long, was shared on Facebook 27,000 times and has more than 20,000 comments, including threats made to the four teenagers who are seen beating the girl up.
Keiblinger said that the police were shocked by the violence shown in the video and understood that other teenagers were angry about it, but warned anyone against making threats on social media. He said police were reading the comments on the video carefully, in case they hold any clues as to why the girl was attacked. Some people have speculated that the violence is part of an initiation for joining the teenagers' clique.
Keiblinger said the video was posted on Facebook by the 15-year-old blonde Austrian girl, as "a warning" to other teens. A social worker from Lower Austria reported it to the police and the victim's sister has also since reported the assault to the police.
Police say the teenagers have already been involved in similar incidents in Lower Austria.
Even Austrian Chancellor Christian Kern expressed his horror after being made aware of the video, writing on his Facebook page: "We cannot accept such a threat to society. Such images and actions, no matter who is responsible, will not be allowed in Austria. The perpetrators must be punished."