"I share the frustration of my Chief Health Officer," she said.
Earlier, the state's Chief Health Officer Brett Sutton slammed the "crap" behaviour on Twitter.
"Some of the behaviour today - when we're asking people to stay home - has been really crap," he wrote in a tweet.
"It's hard to change habits and it's hard to see dangers that aren't apparent yet. But with 3,000 cases of COVID-19 in Australia this week, we're headed to 100,000 in 2-3 weeks without change.
"That means thousands of deaths. Overwhelmed health services. Medical staff at unacceptable risk. Unstoppable spread. Do the right thing now and #StayAtHome. Today. Tomorrow. Until we're through this, please."
Port Phillip City Council closed all of its beaches including the popular St Kilda Beach from Friday.
But there was confusion after the council said walking or swimming was acceptable "as long as social distancing and mass gathering rules are obeyed".
Images of people gathering at Melbourne beaches have been widely shared on social media.
Surf Coast Shire was among about half a dozen other councils to shut down its beaches after people flocked to Ocean Grove, Torquay and Point Addis.
Premier Daniel Andrews has implored people to stay at home if possible.
On Saturday, he introduced on-the-spot fines for people who breach social distancing rules.
Individuals face fines of up to $1,652 for gathering in large groups and businesses could cop penalties of $9,913.
The fines also apply to travellers found to be out-and-about within 14 days of returning from overseas.
Victoria Police said the "vast majority" of people heeded warnings to remain at home, releasing drone footage of quiet inner-city beaches.
The number of Australians who have died after contracting COVID-19 reached at least 16 on Sunday, following the death of two more people overnight.
Australians must stay at least 1.5 metres away from other people. Indoors, there must be a density of no more than one person per four square metres of floor space.
If you believe you may have contracted the virus, call your doctor (don’t visit) or contact the national Coronavirus Health Information Hotline on 1800 020 080.
If you are struggling to breathe or experiencing a medical emergency, call 000.
SBS is committed to informing Australia’s diverse communities about the latest COVID-19 developments. News and information is available in 63 languages at sbs.com.au/coronavirus