Multiple people were arrested at a Melbourne rally on Saturday amid clashes with the police, while protesters also marched through the Sydney CBD and large groups gathered in Brisbane and Adelaide.
Demonstrators in Melbourne voiced conspiracy theories and rallied "against mandatory Covid vaccinations", an idea that has already been rejected by the federal government and health experts.
Asked about the rally, Sutton insisted "fervent anti-vaxxers are really in a small minority".
"They are one and a half, a few percent, maybe, in Australia," he told reporters. "I'm going to ignore them, frankly, and I would encourage you to do the same."
Sutton's comments follow an Australian National University study that found "significant and substantial" increase in hesitancy since the same people were asked about getting the jab in August 2020.
The study found more than one in five Australians indicated they would "probably" or "definitely" not be vaccinated against coronavirus.
Sutton said while true "anti-vaxxers" were rare, he acknowledged a larger group who were were "vaccine hesitant".
"They've seen a vaccine developed over a 12-month period, rather than what might take 10 years," he said. "The reality is it's gone through a really rigorous quality and safety review process.
"It has been in the phase-three trials tested on hundreds of thousands of individuals. It's now been given to over 150 million individuals across the world. Safely."
Victoria's health minister, Martin Foley, said the protests were disappointing and that rallies that pushed "science denialism" were "unhelpful".
Comment: What's also "unhelpful" is calling people fighting for the right to choose their own medical procedures 'science deniers'.
"All the evidence globally shows it is having a significant impact in both preventing the disease and increasingly pointing to its impact on making sure that people do not transmit the disease," he said.
Australia's vaccination program will kick off on Monday, with people in 240 aged care homes across more than 190 locations among those who will be immunised.
Foley confirmed this week that from Monday Pfizer jabs would be distributed to Victorian hotel quarantine workers, airport and port workers, high-risk frontline health staff, and those working who living in public sector residential aged care.
New South Wales and Queensland have also confirmed they will begin vaccinations on Monday.
The federal health minister, Greg Hunt, said no cases of coronavirus were recorded across Australia on Saturday.
There have been no cases recorded in three of the past four days, he added.
On Friday, three cases were recorded in Victoria, all linked to the Holiday Inn outbreak that sparked a five-day lockdown that concluded on Thursday.
Foley said the fact no cases were recorded on Saturday was "positive" and indicated the state was "getting on top of this".
He said there were now 3,000 close contacts from the Holiday Inn outbreak.
Sutton urged Victorians to be vigilant given Covid-19 fragments had been found in wastewater over the past two days.
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