The ACT will institute a territory-wide shutdown within 48 hours.
ACT Chief Minister Andrew Barr said all non-essential services would be closed, following closely on a similar announcement by the NSW Premier.
Schools will also move to online learning, from Tuesday.
"I believe this decision is in the best interest of Canberrans, and will help slow the spread of COVID-19 in our community," he said.
"Despite measures in place to discourage social interaction, there are still too many instances where people are exposing themselves to contracting the virus which is leading to an unsustainable increase in confirmed cases across the country.
"We must also face the reality that, as a territory within NSW, it would be impossible for the ACT to have different arrangements than those in our surrounding region.
"We will ensure that Canberrans continue to have access to the services they need - supermarkets, petrol stations, banks, pharmacies, post offices and convenience stores.
"Freight and logistics will also be considered as an essential service. Over the next 48 hours, we will define these essential services and work closely with retailers on their requirements."
All cafes, bars, restaurants and public places such will be affected by the shutdown.
Details are yet to be announced on bus and tram services.
Also on Sunday Scott Morrison told Australians to cancel school-holiday travel plans.
"All non-essential travel should be cancelled," he said. "It does mean that those holidays that you may have been planning to take interstate over the school holidays, cancel it.
"It is regrettable and I know the impact it will have many people in those communities where those holidays were going to take place...
"That travel needs to be reduced to stop the spread of the virus across the country."
Earlier, NSW announced it would undertake a "comprehensive shutdown" of non-essential services as the number of coronavirus cases in the state rises past 500.
Premier Gladys Berejiklian says supermarkets, petrol stations and pharmacies are among the businesses that will stay open.
Although schools across the ACT and NSW will remain open on Monday, a teleconference with all ACT principals on Monday morning is certain to deliver an instruction that all schools will close at the end of class that day.
"We will be transitioning to an alternate distance education program for most students on Tuesday as well as continuing to provide a face to face education program for those students who need it," Chief Minister Barr said in a statement.
While schools around the ACT have been preparing for this outcome, the suddenness of the announcement will create significant community upheaval.
Justin Garrick, the head of school at Canberra Grammar School, said in a statement, "We are ready should a switch to home learning come."
Speaking shortly before the NSW announcement, Mr Barr said the ACT could not shut its borders because of its close regional connectivity with places such as Queanbeyan and Goulburn "but our region can be protected and we will be working closely with NSW and surrounding local government areas to ensure these measures work effectively".
Mr Barr said all non-essential travel anywhere in the region now must be carefully considered.
"If it is not essential [travel], don't do it," he said.
"This is an unprecedented situation; we must all act together now to ensure we stop and slow the spread of this virus.
"We cannot stress the seriousness of this situation enough for our city, for our country.
"We are doing this to try and save lives."
He said people could expect "more and more tough and stringent rules being put in place in the days and weeks ahead".
The ACT is undertaking an immediate review of all places where people are gathering in numbers.
"If they are on public land, we will be closing these facilities or areas down. If they are on Commonwealth land, we will be asking the Commonwealth to do the same," he said.
He said the ACT government would be carefully analysing the economic measures announced by the Prime Minister on Sunday "to inform our own economic stimulus responses".
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