Officers said the chaos began early yesterday afternoon, after a man was seen driving in erratic circles in the middle of a major intersection in downtown Melbourne.
The driver then turned onto the Bourke Street Mall, which is a pedestrian area.
He began deliberately mowing people down before continuing onto a sidewalk and hitting several others, Victoria state Police Acting Commander Stuart Bateson said.
Police shot the driver and arrested him at the scene.
The 26-year-old man was being treated at a hospital for non-life threatening injuries, police said.
Officials have not released his name and said there was no further threat to the public.
The incident comes amid global concern over extremists using vehicles to strike crowds, following truck attacks in Berlin and Nice, France, last year.
Police Chief Commissioner Graham Ashton said the Melbourne incident had no links to terrorism.
He told reporters that the driver had a history of mental health and drug abuse issues, and an extensive record of domestic violence.
Last weekend, he was arrested after police said he assaulted members of his family.
Officers said that, before the incident in Melbourne, he was involved in a domestic stabbing incident in a suburb earlier yesterday.
Police tried to intercept his vehicle, but called off the chase before he entered the downtown area because he was driving so erratically.
Ashton said they feared a chase through the city might endanger the community. Two adults and a child were killed after being struck by the man’s car, Ashton said. They were not related.
A fourth person died in a hospital last night.
Police did not release any details about that victim.
At least 29 people were injured.
Of those, five were in critical condition, including an infant.
Witnesses have described the chaos that ensued after the vehicle was driven into pedestrians and passers-by.
Sharn Baylis, a tourist from the southern city of Adelaide, said she was on Bourke Street when she mistook the car for an unmarked police vehicle before it started slamming into pedestrians.
“He was just collecting people as he was going along and they were flying like skittles, basically,” Baylis said.
“He was just driving in a really determined fashion, just in a straight line.
“There was no hesitancy as he got to the crowds and he didn’t swerve, it was just – he just drove through them.” Video footage shot from a news helicopter showed several officers standing over a man lying on the sidewalk, clad only in his underwear, his hands apparently handcuffed behind his back.
A video posted on social media captured the moment the car began driving in circles in the intersection before continuing on toward Bourke Street.
The driver could be seen hanging out the window, apparently shouting.
The crisis unfolded at a particularly busy time in Melbourne, which is hosting the Australian Open tennis championship.
Officials said the event was continuing as normal. On 19 December, a truck was deliberately driven into the Christmas market beside Kaiser Wilhelm Memorial Church at Breitscheidplatz in Berlin.
The terrorist attack left 12 people dead and 56 others injured. The perpetrator was Anis Amri. Four days after the attack he was killed in a shootout with police near Milan in Italy.