* Two people arrested - police
* Ambulance service says child suffered serious head injury
* Incident occurred near busy train station entrance
Police said the motive for the incident was not known but it had chilling echoes of several attacks by Islamist militants in various parts of the world over the past two years.
In January, four people were killed and more than 20 injured when a man deliberately drove into pedestrians at a spot just a few hundred metres away from the Thursday incident, though that incident was not terrorism-related.
A witness told the Australian Broadcasting Corp the vehicle was travelling at 80 to 100 kph (50-62 mph).
"There was no breaking or any slowing down at all," said Jim Stoupas, who said he was standing outside his donut shop when the car crashed into the people, one after another.
"All you could hear was just 'bang bang bang bang bang'," he said.
Police said they had arrested two men but that they had not been charged.
"We believe based on what we've seen that it was a deliberate act," Victoria Police Commander Russell Barrett told reporters.
"The motivations are unknown," Barrett said.
The Victoria State ambulance service said it had taken 13 people to hospital, including a pre-school child with a serious head injury.
Police did not identify the two arrested men but pictures taken at the scene and posted on social media showed a bearded man in a flannel shirt sitting on the footpath and talking to police.
Major streets in Australian cities have been packed with Christmas shoppers this week.
The incident took place on Flinders street, a major road that runs alongside the Yarra River, in the central business district of Australia's second-biggest city.
Prime Minister Malcolm Turnbull said federal and state police as well as security agencies were working together to secure the scene and investigate the "shocking incident".
"Our thoughts & prayers are with the victims & the emergency & health workers who are treating them," Turnbull said in a post on his official Twitter account.
Victoria's premier, Daniel Andrews, writing on his official Twitter account, called it a "horrible incident".
Melbourne has installed about 140 concrete bollards in the city centre to stop vehicle attacks by militants.
Sydney, Australia's biggest city, has installed concrete barricades in main pedestrian thoroughfares.
Authorities in cities around the world have taken similar measures following attacks in Europe and the United States.
Australia has been on a "high" national threat level since 2015, citing the likelihood of attacks by Australians radicalised in Iraq and Syria.
A staunch ally of the United States and its campaign against the Islamic State group in Syria and Iraq, Australia believes more than 100 of its citizens are fighting there.
Two hostages were killed during a 17-hour siege by a "lone wolf" gunman, inspired by Islamic State militants, in a cafe in Sydney in December 2014.
Thumbnail Credits : Reuters