It will become mandatory from 11.59pm on Wednesday 22 July, Mr Andrews said.
People who are out of the house and not wearing a mask can be fined $200 by police, he added, while urging residents to adopt a "commonsense" approach.
There are some reasons for not wearing a masks such as medical reasons, children aged under 12, a professional reason or if not practical - like running - but individuals need to carry a mask with them.
Teachers won't need to wear a face covering while teaching but students there for VCE, VCAL or for onsite supervision will. Everyone is expected to wear one on the way to and from school.
"Now, commonsense will guide this," Mr Andrews said.
"If you're out running, part of your daily exercise, then it may not be practical to wear the mask while you are running. But you should bring the mask with you and you should wear it before and after you have gone for your run.
"There'll be some other environments, for instance, where you're going into a bank, when you would need to take your mask off."
Up to three million face masks are on order by the state government and the first batch of 300,000 is due to arrive this week, he added.
"Most of us wouldn't leave home without our keys, we wouldn't leave home without our mobile phone, you won't be able to leave your home without the mask and then where it is absolutely essentially to stop the spread of this virus," Mr Andrews said.
Health Minister Jenny Mikakos on Sunday also announced that Victoria would be extending its current state of emergency until 11.59pm on 16 August.
"That decision has been made acting on the advice of the chief health officer, given that we continue to see rising case numbers, increasing numbers of people being hospitalised and sadly also increasing fatalities," she told reporters.
Ms Mikakos urged people to improvise if they were unable to secure an appropriate mask in time.
"Don't be stressed or anxious if you cannot get your hands on a top-tier surgical mask, you can make one yourself," she said.
"You can use a scarf, you can use a bandanna, something is better than nothing."
Chief health officer Brett Sutton described Victoria's situation as a "numbers rollercoaster", after a record spike in infections on Friday followed by a substantial dip on Saturday.
Dr Sutton stressed the importance of wearing masks to help control the outbreak.
"These won't always be really easy and they won't always be welcome, but they are important, and there are lessons, increasingly internationally, that the jurisdictions that are doing well have introduced mandatory mask wearing," he said.
"Those that haven't, are the ones that are seeing really catastrophic numbers at the moment."
New rules for aged care
The Victorian government on Sunday also announced new rules to try and keep the virus from spreading through the state's aged-care homes.
Funding would be provided to limit the movements of aged-care staff across different facilities, Ms Mikakos said.
"We have been seeing a significant number of outbreaks in our aged care sector and these are the most vulnerable people in our community," she said.
"We have seen specific instances in recent days of staff who have worked across multiple facilities and then we have had multiple outbreaks across those facilities.
"So the package will involve workforce funding support... to ensure that employers can minimise the movements of staff across facilities."
Aged-care workers without access to leave entitlements would also qualify for a $1500 hardship payment if they were required to self-isolate, Ms Mikakos said.
Residents in metropolitan Melbourne are subject to stay-at-home orders and can only leave home for essential work, study, exercise or care responsibilities. People are also advised to wear masks in public.
People in Australia must stay at least 1.5 metres away from others. Check your state’s restrictions on gathering limits.
If you are experiencing cold or flu symptoms, stay home and arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080.
News and information is available in 63 languages at sbs.com.au/coronavirus