In Melbourne, mounted officers used pepper spray when elements of a 4,000-strong rally broke through police lines.
Police arrested 218 people, and at least seven officers were injured.
In Sydney, where lockdown measures have been extended for another month, more than 1,000 officers dispersed protests.
It came as the state of New South Wales (NSW), of which Sydney is the capital, recorded 825 new locally-acquired cases, the highest number for any Australian territory in a 24-hour period.
In Brisbane, the capital of Queensland, more than 2,000 protesters gathered before holding a largely peaceful march.
Police in the state of Victoria condemned the violence that broke out in Melbourne on Saturday.
"While there were some peaceful protesters in attendance, the majority of those who attended came with violence in mind," a spokeswoman said, quoted by the Sydney Morning Herald.
"The behaviour seen by police was so hostile and aggressive that they were left with no choice but to use all tactics available to them."
All those arrested face fines of A$5,452 (£2,850) for breaching Covid regulations, police said. Three people were also charged with assaulting police.
Stay-at-home orders were extended across Victoria on Saturday in a bid to contain a widening outbreak of Covid cases.
The protests in Sydney were smaller, with about 250 people taking part.
Deputy NSW Police Commissioner Mal Lanyon told reporters that one officer had been injured after being dragged into a road by a protester and that 47 arrests had been made.
He said police had stopped about 38,000 cars heading into the city centre and handed out 260 infringement notices to people across the state suspected of breaching lockdown regulations. He called the actions of the protesters "deplorable", saying the police response was not about stopping free speech but stopping the spread of coronavirus.