The city's library, art gallery and Archie Graham Centre closed their doors on Monday and the council's officers were closed to the public, although mayor Tony Herbert said the phones were still being manned.

Campsites at the council-run holiday parks would close and cabins made available on compassionate grounds.

He said a number of council staff were working from home, and preparations were being made to allow more people to do that.

AquaZone has also closed and The Lighthouse Theatre performances halted.

Cr Herbert said the library would remained closed until at least April 14.

The council's chief executive officer Peter Schneider said the library would automatically extend the due date of all loans to April 24.

Fines will be waived for all library materials returned until further notice, the after-hours return chute will remain open and library staff will be available to answer phone inquiries.

"We know that people will miss these great Warrnambool institutions but the advice from the Department of Health and Human Services on non-essential services means that we must close these sites to help stop the spread of COVID-19," Mr Schneider said.

"We will also be closing down powered and unpowered campsites Surfside Holiday Park.

"Surfside cabins will be made available on compassionate grounds and for people who require accommodation as they transit home.

"Our child care service is operating for now and we are seeking advice from the department in relation to our vacation care program that usually operates in the Warrnambool Stadium.

"The Archie Graham Community Centre is closed to the public but a small number of staff will be based there to organise essential services such as meals on wheels.

"The Civic Centre in Liebig Street is closed to the public but people can still call Council on 5559 4800.

"We also provide a "live chat" function through our website www.warrnambool.vic.gov.au and people can also lodge a request online at www.warrnambool.vic.gov.au/lodge-request"

Cr Herbert said the council was also in discussions about launching a "Get Around Warrnambool" campaign to help support businesses.

He said the aim of the campaign would be to encourage people to spread their shopping opportunities around as many Warrnambool businesses as possible.

"That will be the message. Sure there are some items that only the supermarket stocks, but there will be a number of local businesses that remain open for either take away or home delivery," he said.

The Prime Minister Scott Morrison announced tough new measures to drive home the social distancing message on Sunday night in response to the growing spread of the virus, and after images of beachgoers ignoring social distancing measures emerged at the weekend.

But Cr Herbert said it was obvious today that Warrnambool shoppers were taking the social distancing message seriously.

He said the council was holding an urgent council meeting on Monday night and one of the items on the agenda was free parking.

The mayor urged residents to heed the health warnings and reminded people to wash their hands.

"If people are out and about, and we understand it's very difficult for some people to think about remaining home for big lengths of time, that they really do their best to adhere to these social distancing requirements," he said.

He said the images of people not practising social distancing on Bondi Beach over the weekend were a wake-up call for people.

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