The car “collided with a number of pedestrians” on Flinders Street, a busy junction in the center of the city, said Victoria Police.
Police have arrested two people and said it was a deliberate act but is too early to say whether it was terrorist-related.
“The motivations are unknown,” police commander Russell Barrett said.
The white SUV struck pedestrians just after 16:30 local time.
Victoria Ambulance said in a statement that a child of pre-school age with serious head injuries was among those taken to hospital.
Prime Minister Malcolm Turnbull said that the investigations had begun, and sent “thoughts and prayers” to those affected.
He tweeted: “As our federal & state police & security agencies work together to secure the scene and investigate this shocking incident our thoughts & prayers are with the victims & the emergency & health workers who are treating them.”
In January, six people died when a man drove a car into pedestrians on Bourke Street.
Afterwards, Melbourne authorities installed concrete blocks in various locations – including on Flinders Street – hoping to prevent vehicle-based attacks.
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