A staff member was positioned at the front of the Gungahlin store on Monday morning, handing out surgical masks to customers as they entered.

Although face masks are not compulsory, the supermarket giant said encouraging mask use was a step the business could take to protect the community, and normalise it.

Most customers accepted the masks on offer, with only a handful of people coming to the store prepared.

Many shoppers hastily removed the mask as soon as they left the store.

One customer, Taylor, has been wearing a mask throughout the pandemic because she lives with a person who is vulnerable to coronavirus.

She was glad Woolworths had taken action which surpassed current ACT health advice and said it was important to protect vulnerable people.

She said one of the biggest barriers to wearing a mask was feeling out of place as they are not currently recommended in Canberra by ACT Health.

However, Chief Minister Andrew Barr said ACT residents would be required to wear face masks if COVID-19 cases were detected in Canberra or the surrounding region.

"Canberra is not an area of high community transmission and, therefore, the wearing of face masks is not currently a mandatory requirement," Mr Barr said.

On Sunday, NSW Premier Gladys Berejiklian strongly recommended masks be worn in areas where social distancing could not be guaranteed and for customer facing workers.

The mask guidance applies across all Woolworths Supermarkets, Woolworths Metro Food Stores, Big W, Dan Murphy's, BWS and ALH Hotels in ACT, NSW and Queensland.

Across the road, at Big W Gungahlin all staff members were wearing masks but they weren't offered to customers on entry.

Other supermarkets, including Coles, have not followed Woolworths' lead. A spokeswoman said the company would continue to follow state or territory government health advice.

Masks were scarcely seen at Coles Gungahlin on Monday, which was notably busier than its counterpart.

Coles customer Ursula McCormack has been using a mask when doing the groceries or in shopping centres for some time.

She said she was in a high-risk age group for COVID-19 and wanted to reduce the risk of infection.

"I have a mask in my handbag," she said.

"As soon as I get my trolley I'll be putting it on."

Ms McCormack said although she would like to see other supermarkets urge mask use, it wouldn't determine where she went to shop.