Minister for Health Stephen Donnelly has said there will be "very little need" to police the wearing of face coverings as he believes the public will comply with the new coronavirus regulations.
Face masks will become mandatory in all shops and retail centres from Monday.
Mr Donnelly said the vast majority of people are already wearing face coverings in public.
Staff in retail stores are able to ask customers to wear a covering before entering the shop.
It comes after the Government said plans to reopen pubs next week have been put on hold.
Pubs, bars, hotel bars, nightclubs and casinos will remain closed until a review at the end of the month.
Mr Donnelly told RTE Morning Ireland on Wednesday that he understands the frustrations of business owners but the decision had been taken to avoid another lockdown.
The minister said gardai will be used as a last resort to police the wearing of face masks.
He added: "In the first instance I imagine there would be very little need for policing. We asked people to wear face coverings on public transport and there was huge compliance.
"I think most of us see when we go to shops the vast majority of people are now wearing face coverings as an additional public health measure to suppress the virus.
"We're putting it on a statutory footing from Monday. My hope is that the vast majority of people will comply, inevitably some people will forget.
"We've all got to build it into our habits, so in the same way as we check we've our keys and we've our phones, we now need to be checking that we've got a mask in our pockets.
"I envisage that there would be very, very little need for the gardai.
"The reason that our fatality rates are not a lot higher than they are is because of the extraordinary solidarity that people have shown every time they go into the shops, every time they put on a mask, nearly one-and-a-half million people have downloaded the (contact tracing) app.
"The message from public health now is we need to focus on the basics - wash our hands, maintain social distancing and just follow the basic public health advice."
Meanwhile, Health Service Executive boss Paul Reid said he appreciates the "genuine disappointment and frustration" of bar and business owners.
He posted on Twitter: "But I also just want to thank our public health and contact tracing teams who are doing a super job protecting us by managing outbreaks.
"This is a nasty and viscous virus."
