Inspector Shane Brundell said most people were doing the right thing. But police were concerned by fights filmed in other Australian supermarkets, which had been shared on social media.

"I have tasked our local police here to increase their presence around supermarkets and the carparks," Inspector Brundell said.

He said people fighting in supermarket aisles and car parks would be arrested and held accountable.

"We will not tolerate that... there is no reason for it. The panic has to stop," Inspector Brundell said.

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He urged people to calm down, and to look after each other and themselves.

"We will get through this together," he said.

He said Victoria Police had powers to assist the Chief Health Officer and the Department of Health and Human Services if requested and needed.

It was not clear what those powers would look like.

"Police will be operating with discretion, though... We don't want to be exercising these powers and we won't have to if the community do the right thing," Inspector Brundell said.

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He flagged the potential for temporary closures of police stations, should they be impacted by the virus.

Inspector Brundell said Victoria Police had contingencies in place.

"We have tested those plans and we believe we are in a good position to continue providing a service to the community, as we always have," he said.

He said local police stations were open and operating as normal.

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