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Protesters began gathering in the city centre in separate groups on Wednesday as the state's Police Chief Commissioner Shane Patton vowed to prevent more violent protests but declined to discuss the measures planned to control violence or unruly behaviour.
"I'm not going to talk about the tactics we'll deploy today," Patton said at a media briefing in Melbourne, the state capital.
"I want them to be completely unaware of what we're going to do and what capacity they may face."
Television footage showed crowds of protesters walking in the middle of streets in different parts of the city, with police sometimes giving chase.
"There has been a couple of arrests so far," Deputy Commissioner Rick Nugent told radio station 3AW.
Sydney and Melbourne, Australia's largest cities, as well as the capital Canberra have been in lockdown for weeks to contain a Delta outbreak. Melbourne is in its sixth lockdown, the most of any Australian city since the pandemic began.
Authorities are aiming for a staggered reopening in Sydney and Melbourne, easing some curbs when the adult population reaches 70% fully vaccinated, expected next month. More restrictions will be relaxed when the figure hits 80%.
The rates of people age 16 and older who are fully vaccinated were 54% in New South Wales and 45% in Victoria.
Even as officials pledged more relaxation of restrictions within weeks, the traditional New Year's Eve firework display in Sydney at 9pm was cancelled for a second year in a row. But the midnight fireworks will likely go ahead.
A City of Sydney spokesperson said they want to limit the "mixing of crowds" between the two separate events.
Victoria reported 628 new local cases on Wednesday, the year's biggest one-day rise, exceeding the previous high of 603 a day earlier.
A total of 1035 new infections were recorded in New South Wales, home to Sydney, up from 1022 on Tuesday.
Australia's Covid-19 numbers stand at around 90,300 infections, including 1186 deaths. Eight new deaths were reported in the country.