Andrews has urged people not to come together, be it for celebrations or protests.
“It’s not about what you’re meeting for, it’s about, are you meeting in a safe way?” Mr Andrews said.
“(The Invasion Day march) is not a sitting event and the judgment of the public health team, not the politicians, could not be made safely.”
Opposition leader David Davis called Andrews’s approach a “clear double standard.”
But a service will be held at dawn on “Invasion Day”, with the backing of Melbourne City Council.
“I don’t think the world should stop because of COVID, we just have to do it differently,” said Jill Gallagher, a former Treaty Commissioner.
“It remains important to convey a message about what Australia Day means to us as Aboriginal peoples.”
Outdoor gatherings in Melbourne are currently limited to 100 people, but exemptions can be granted for public events as long as the organizers submit a COVID safe plan.
All attendees must be registered and must maintain social distance.
“The sunrise ceremony is a way to support an event that reflects that ancient Australian history,” said Melbourne Mayor Sally Capp.
The service at Kings Domain will be broadcast to 250 seated people with COVID council and marshals organization QR codes.
Intelligence services have suggested that people on both sides of the political spectrum are planning protests.
“There will be zero tolerance for any antisocial or criminal behavior,” said a Victoria Police spokesman.