Officials said they had tested about 15,000 people in the area and all had come back negative.
“This is one of the best outcomes we could hope to see,” said Jeroen Weimar, Commander of Testing and Community Engagement for Victoria.
Andrews is under intense pressure to lift Melbourne’s lockdown, imposed in July. Businesses and the federal government argue it will delay Australia’s economic rebound.
Australia’s economy shrank 7% in the three months to the end of June, the biggest quarterly shrinkage since records began in 1959. The unemployment rate hit a 22-year high of 7.5% in July as businesses and borders closed to deal with the coronavirus.
Prime Minister Scott Morrison has highlighted the fact that neighbouring New South Wales has much looser restrictions despite regularly reporting higher daily case numbers.
Australia has so far recorded just over 27,500 COVID-19 infections, far fewer than many other developed countries.
Victoria, which accounts for more than 90% of the 905 deaths nationally, did not record any new deaths from the virus in the past 24 hours.