His comments come as the Victorian Government announced Goulburn Valley Health would become the site of a new public health team dedicated to monitoring COVID-19 cases in the region.
While there was only one active COVID-19 case recorded in Greater Shepparton, Mr Andrews said he would not "hesitate to act" if there was evidence people travelling from lockdown areas were causing a spike in regional Victoria's cases.
"We're always happy to to go further, if the evidence says that people are not behaving as they should," he said.
People are permitted to travel in and out of lockdown areas for essential reasons, including work and accessing health services.
Mr Andrews said while most people were doing the right thing, some were trying to get around lockdown restrictions, such as enrol their children in regional Victorian schools.
"We've said no to that - you can only be enrolled at one school," he said.
Mr Andrews said people wanting to inspect property in regional areas should have a "pretty good case" to justify it.
"(And) there's no need to be traveling to regional Victoria to buy goods and services that you can get in Melbourne," he said.
"Everyone has a shared interest in these numbers in regional Victoria remaining low."
Sixteen Shepparton police officers remain in self-isolation after coming into contact with a Melbourne police member who tested positive for COVID-19.
"My advice from Victoria Police (is) this is not the first member of Victoria Police that's tested positive," Mr Andrews said.
"That's why Victoria Police have got more recruits and they've ever had, so they can move people around."
The Victorian Government has announced increased COVID-19 testing hours at Goulburn Valley Health, and has encouraged all regional Victorians to wear masks if unable to socially distance in public places.
Goulburn Valley Health will also be the site of a new public health team dedicated to tracking and following up COVID-19 cases in the region.
Mr Andrews said regional areas would see more asymptomatic testing in the weeks and months to come.
Greater Shepparton has not seen an increase in active cases, remaining on one.
Victoria recorded its highest spike yet, recording 428 new cases in a day.
But the overall number increased by 415 after 13 cases were reclassified.
Mitchell Shire has 16 active cases, while Moira Shire, Campaspe Shire, Strathbogie Shire and Benalla Rural City don't have any.
Three new deaths were reported - a woman in her 80s, a man in his 70s and a man in his 80s.
The death toll is now 32.
There are 122 people in hospital with coronavirus, including 31 in intensive care.
Victoria has had 5165 cases in total - 2462 are currently active, and 2669 people are recovered.
Of the total number, 313 are in regional Victoria.
More than 1,250,000 tests have been processed.
