The Tánaiste has warned that retailers using health regulation loopholes to stay open will face enforcement action.
Leo Varadkar said he received confirmation on Sunday that mixed retail stores that do not abide by the new legislation are subject to penal regulations.
As part of Ireland's lockdown restrictions, only shops selling essential items are allowed to open.
Under government guidelines, retailers that have "discrete spaces" for essential and non-essential items have been told to separate the areas.
A number of businesses, including some sports and shoe shops, have remained open because they sell PPE and face masks, but Mr Varadkar said non-essential items must be closed off to the public.
"You need to abide by the regulations and abide by the spirit of the regulations," he told RTÉ.
"If you are a mixed retailer you should separate your stock and only sell items that are essential. If you are a big store that has groceries and clothes, you have to separate the clothes. General workwear is OK but not other clothing.
"We have been in touch with the Garda about that. If they are using PPE to sell other products then that is different.
"It's also unfair - think of all the small shops and retailers that have to close - it's unfair on those and it won't be allowed.
"Having engaged with the Department of Justice I am confident the law is strong enough."
He warned that gardaí will enforce the legislation.
Mr Varadkar also said he is confident shops will reopen in December.
"It is early days but it seems the Level 3 restrictions are starting to have an effect. We are seeing the cases level off and the positivity rate fall, but we have yet to see the effect of Level 5 restrictions.
"I am confident we will be able to get to Level 3 in December and that would mean shops opening again, but we can't be complacent.
"Often when you tell people things are getting better then they relax, but this virus is spreading like wildfire."
He also said that while the country could be plunged into Level 5 again early next year, it is not inevitable.
The Fine Gael leader said the Government is "increasingly optimistic" a vaccine will be approved in the next couple of months and it will be possible to start vaccination early next year.
"This is based on information coming to us both from (testing) companies and statements from WHO (the World Health Organisation)," he added.
It comes as Health Service Executive (HSE) boss Paul Reid said the positivity rate in testing for Covid-19 has dropped.
He tweeted: "The positivity rate in testing has now come down over the past eight days.
"The number of close contacts is now down to an average of three.
"Most close contacts are household. Still very early but good.
"We're all be part of the solution. Let's keep this going."
Sinn Fein's justice spokesman Martin Kenny criticised how the Government handled legislation to enforce new restrictions.
He said it was rushed through the Oireachtas without proper scrutiny.
"The vast majority of people are compliant and working with the rules, there's a tiny amount of people who are blatantly trying to break the rules, and of course there needs to be enforcement there," he told RTÉ's The Week In Politics.
"We are opposed to this legislation because of the way it was brought in, the way it was rushed through, the way there was no amendments taken.
"We felt that was totally inappropriate, and it would also go against what the Garda are saying, that they are trying to encourage and help people and in most cases they are able to do that, and they haven't asked for these fines to be brought in.
"The way the Government has handled this has been most unfortunate."
Minister for Agriculture Charlie McConalogue defended the Government's handling of the legislation.
"The legislation was to, in cases where people are not doing their bit, that there would be powers in place to enforce that," he said.
"The approach being taken is to communicate and ask everyone to work together."