But the impact of any measures on Warrnambool's cultural spaces such as Flagstaff Hill or the Lighthouse Theatre are not yet fully known.

Warrnambool City Council chief Peter Schneider said the council would review whether a number of events planned for coming days would go ahead.

Moyne Shire Council shut its Port Fairy visitor information centre on Monday with all services now online.

But council chief Bill Millard said customer service centres would remain open, though asked people to do their business online if possible.

"Council's aged care, day care and kindergarten services will continue to operate as normal," Mr Millard said.

"Any non-essential council-run external events or meetings will be postponed ... next week's ordinary council meeting will proceed as planned, though public attendance is not encouraged."

Glenelg Shire will temporarily shut its visitor information in Portland, Casterton and Nelson until further notice, the council said in a statement.

It has also cancelled any upcoming council events or public meetings.

The council says its library service will be significantly reduced, with no access to public computers, meeting rooms and public events cancelled.

Youth programs including the L2P Learner Driver program, mental health first aid training sessions and the school holiday program are also cancelled.

The Portland Arts Centre will remain open, but any upcoming arts programs and events are postponed, the council said.

Its statement said cash refunds would be offered to anyone who purchased tickets to What's New Pussycat from 2pm to 3pm tomorrow, while over-the-phone refunds are also available.

The council's customer service centres will remain open and its aquatic facilities, home and community care services and early learning programs will operate as usual.

We have removed our paywall from our stories about the coronavirus. This is a rapidly changing situation and we to make sure our readers are as informed as possible. If you would like to support our journalists you can subscribe here.