Saeed Noori, who has a history of drug abuse and mental problems, allegedly drove his car through a busy downtown intersection on Thursday, careering into tourists and shoppers.
His motive is not clear, although police allege he made "utterances" to them about voices, dreams and the "poor treatment of Muslims" after his arrest.
No link to any terrorist group has been found.
"A 32-year-old man has been charged with 18 counts of attempted murder and one count of conduct endangering life," Victoria state police said in a statement, citing Thursday's attack.
Broadcaster ABC said Noori did not apply for bail when he appeared in court on Saturday, putting his head in his hands and becoming emotional when he saw his mother weeping during the short hearing.
The magistrate ordered a psychiatric assessment and he is due to appear in court again on Wednesday, the broadcaster reported.
Of 19 people taken to hospital after the incident, 12 remain, with three in a critical condition.
Nine foreigners were hurt, including three South Koreans, two of whom are fighting for their lives. The others were from China, Italy, India, Venezuela, Ireland, and New Zealand.
"Police are very well placed to do everything that is necessary to keep venues like the MCG (Melbourne Cricket Ground) safe and so many others that are going to be really busy over these coming days," Victoria state Premier Daniel Andrews said.
Thursday's incident came after a car rammed into pedestrians in Melbourne's busiest mall in January, killing six people. The driver, whose case is still being heard, was a drug addict who had allegedly just stabbed his brother.
Like other countries, Australia has been taking steps to prevent vehicle attacks in crowded public places since the Nice truck incident in southern France last year that killed 86 people.
They include deterrent options like fencing and closed circuit cameras, and using delaying tactics such as trees and bollards to slow down vehicles.
Melbourne has also been installing a public siren system to warn people of possible terrorist attacks or other serious threats.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.