The driver has been arrested, though police say there were no indications the attack was motivated by terrorism.
The horrific scene took place at 12:30 today and police have allegedly arrested a 26-year-old man who they claim has Bosnian roots.
Part of the city was sealed off, with large numbers of ambulances and helicopters sent to the scene.
Local media has reported that after driving the SUV into the crowd, seemingly targeting people at random.
After the vehicle stopped the man left it and used a knife to attack several people.
The man, who reportedly hit a cyclist before his car went into the crowd, acted alone according to police.
The square in Graz was hosting an event related to the Austrian Formula 1 Grand Prix, which is being held nearby.
The regional governor confirmed that three people had died and 34 were injured, some seriously.
Hermann Schuetzenhoefer told reporters that the suspect was a 26-year-old man who was “mentally unbalanced”.
“There is no explanation, there is no excuse,” he added.
Austrian Chancellor Werner Faymann also said he was deeply shocked by the incident.
Sixty ambulances and four helicopters were sent to the scene.
Graz Mayor Siegfried Nagl, who witnessed the incident, told Kleine Zeitung newspaper: “The driver deliberately drove into pedestrians. I myself saw a woman being run over.”
The Austrian Grand Prix takes place this weekend in Spielberg, and it is thought that many of the city’s emergency services had been deployed there.
Graz mayor has cancelled all city events in the city and ordered black flags of mourning to be raised above municipal buildings, AP reports.
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