Victoria police said six officers required hospitalisation during the violence on Saturday. Several officers were knocked to the ground and trampled, the police said and television footage showed.
“What we saw today was a group of protesters that came together, not to protest freedoms, but simply to take on and have a fight with the police,” Victoria Police Commander Mark Galliott told media.
The illegal gathering comes as the city goes through its sixth lockdown since the pandemic started, with the state of Victoria reporting more than 500 cases of COVID-19 on Saturday.
Footage from one incident showed a crowd charging through a police line as scuffles erupted along a tram route.
In Sydney, riot squad officers, highway patrol, detectives and general duties police were also deployed to the streets, preventing large gatherings.
Australia has been grappling with an outbreak of the Delta variant of the coronavirus since mid-June, with both Sydney and Melbourne, and the capital Canberra, in strict lockdowns for weeks now. On Saturday, 1,882 new coronavirus cases were reported, most of them in Sydney.
Most of the restrictions in Victoria, New South Wales and Canberra are to remain until at least 70 percent of those aged 16 or older are fully vaccinated, which based on the current pace of inoculations could be achieved in late October or early November.
A high rate of compliance with public health orders has helped Australia keep the number of infections relatively low, with just below 85,000 total cases and 1,145 deaths since the start of the pandemic.
The vast majority of Australians support vaccinations and public health measures, but there have been sporadic and sometimes violent protests against the management of the pandemic.