Witnesses said the man had dragged a woman from a taxi, and started firing a handgun when two men came to her aid.
Ross Murchie said he saw a man holding a screaming girl by the hair while coming out of a building.
"She tried to grab hold of a taxi that was going by and the couple of bystanders went over to ask what was happening," he told ABC. "He let go of her hair, pulled out a gun and shot them all."
The man then fled on foot.
Police said the woman and one of the men who went to assist were rushed to hospital in critical condition with gunshot wounds to their chests, while the third victim died at the scene.
Inspector Glenn Weir told local media a large operation was under way "as we speak to try and apprehend the offender".
"It certainly appears as though there was some verbal confrontation prior to the shooting between the male and the female, so it appears as though there was some relationship between those two people," Weir said.
Australia significantly tightened its gun-control laws after the Port Arthur massacre on April 28, 1996 when 28-year-old Martin Bryant killed 35 people and wounded 37 in Tasmania in the country's worst shooting incident.