"If we don't get this right, if the rules aren't followed, then I will have no other option than to shut you down," Mr Gutwein said on Monday.

Coronavirus: All the latest updates on COVID-19 for Tasmania

Mr Gutwein urged Tasmanians to consider the reasons why they are leaving their homes.

"Going out and purchasing supplies is one thing, but going out and browsing and having a family outing is entirely another," Mr Gutwein said.

"It is entirely unacceptable and, to be frank, it is irresponsible in terms of the health of the community, the health of your family and those that you love.

"Please stay home and save lives."

Mr Gutwein said he was aware of the community concern surrounding the number of people attending supermarkets and other retailers.

"I note that today Coles and Woolworths have announced they will be introducing new rules for Easter, only allowing set numbers into their stores. A one-in, one-out policy with people queuing outside," Mr Gutwein said.

"This type of sensible management needs to extended across all retail stores.

"Maximum numbers should be based on the social distancing policy [of] four square metres per person based on aisle space, of the space people can actually move about in, not just on the total gross floor space.

"Queuing stations need to be identified and clearly set out outside of these larger stores.

"If carpark space needs to be given up to ensure that you've got space so that people can appropriately socially distance we would expect you give up carpark space.

"If security is required to assist you it is our expectation you employ appropriate security as well."

Mr Gutwein said if social distancing measures were not adhered to he would be looking at classifying essential and non-essential retailers, with non-essential stores to be closed.

The Australasian Association of Conveniences Stores, which represents 200 Tasmanian outlets, said it wanted to reassure the public it was taking seriously the need to ensure social distancing rules were applied in stores throughout the state.

AACS chief executive Jeff Rogut said members have introduced strict hygiene standards to mitigate the risk associated with the spread of disease, including extensive store signage, hand sanitisation cleaning stations, frequent disinfecting of surfaces and the provision of single use plastic gloves.

"Convenience stores provide essential services such as fuel but also necessities such as bread and milk as well as a range of other grocery items that are essential to the daily needs of Tasmanians, often in areas not serviced by large supermarkets and the like," Mr Rogut said.

"We believe by having a diversity of convenience store retailers providing essential services throughout Tasmania, the interactions are spread wider in more sparsely occupied retail outlets and so help to reduce the spread of COVID-19 as opposed to cramming them all into the local major chain."