Thirty-four were injured in the incident, in which some are seriously hurt, and now still in critical condition. One of the three victims who died was a 7-year-old boy, Xinhua reported.
The witness of the incident said the car went into the crowds in the city center at a very high speed.
The driver of the car is a 26-year-old man who have been arrested by police, and is suspected of having psychosis.
Austrian official said initial investigations indicated the incident was not terror-related. The local government sent around 60 ambulances to the scene.
Graz is Austrias second largest city, and the capital of Steiermark, a southeastern state of Austria.
The incident happened at around noon, when the mayor of Graz, was riding a Vespa only meters away from the car as it went down the street.
The city center, where the incident took place, is Grazs main shopping street.