It comes amid widespread reports that people from out of town have been travelling to regional and rural areas to purchase items unavailable in Melbourne.

Federal Member for Bendigo Lisa Chesters said she was aware of some Bendigo and Woodend stores that have been affected.

"It is unfortunate that we have had people come up from Melbourne in minivans and buses to shop here in our local area," she said. "That creates extra stress in our network.

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"But what I understand from local managers in our supermarkets, they're feeding that back to Melbourne to try and get more deliveries back up this way.

"It's hard for us to control, it's hard for us to stop. People are free to shop where they like."

A Riddles Creek supermarket has told customers it would begin checking IDs of shoppers to ensure they lived in the area.

The Foodworks store posted on Facebook that it had "no other choice but to enforce very strict restrictions".

Other supermarkets in central Victoria were yet to introduce similar measures.

Ms Chesters said people just needed to remain calm and respectful when doing their grocery shopping.

"All we're asking people is to be their very best self, not their worst self," she said. "Look out for one another, be more community minded.

"I know that the supermarkets are trying to police it where they can but they have no real power or authority over that."

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Both Woolworths and Coles have been opening an hour early this week for elderly customers or people with a disability.

The major supermarkets have also cancelled click and collect, and home delivery options for customers, leaving some people unable to access items.

Ms Chesters said both state and federal governments were working to ensure those people were supported.

"We're speaking to our local welfare agencies," she said. "They're looking at ways they can keep their services open and continue to provide foods and the basics.

"We understand the state government is going to set up a care package arrangement for people who can't get out of their home. So we are working towards a solution."

Dozens of shoppers lined up before 7am at a Bendigo Coles store on Wednesday in the pursuit for toilet paper. Many left within ten minutes without being able to purchase the illusive item.

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