The final authority on wearing face coverings in shops and other indoor settings rests with An Garda Síochána.
That is according to the director of Retail Ireland.
The wearing of face coverings in shops and other places like hairdressers, cinemas and museums is now mandatory.
But Arnold Dillon told Newstalk Breakfast it will not simply be a case of no mask, no entry to shops.
"Retailers will be actively encouraging the public to abide by these new rules, but there will be certain exemptions and the rules don't apply to everyone.
"So not everyone in a shop will necessarily be wearing a mask - but we do expect very positive and good compliance.
"I think over recent days, since the announcement that face coverings would be mandatory, we've seen a major increase in the usage in retail.
"I think people going into shops over recent days will have noticed that.
"And I think from today we'll expect really good compliance right across the retail sector."
He also explained that staff on the shop floor will be wearing masks, while those behind screens will not.
Asked who will police the wearing of masks, Mr Dillon said: "We did have some significant concerns when this new move was first mooted.
"And I think what we want to avoid is a situation which unfortunately we've seen in other countries, and a very tragic situation for example in France."
"I think what we have now with the new rules is a very sensible approach: the retailers are mandated to actively encourage and support the use of masks.
"But the ultimate authority in terms of enforcement are the Gardaí.
"I think what that will do is give retail workers the flexibility to actively encourage their use, but to be able to avoid situations and - potentiality dangerous situations in a minority number of cases I'm sure - where we could have a dispute with staff and customers on this".
"It is a concern, but I think what we do have in the rules at the moment is a level of discretion with the staff."
Regulations to enforce the compulsory wearing of face coverings on public transport came into effect last month.
Taoiseach Micheál Martin has said retail staff will be required to wear face coverings, unless there is a partition or a space of two metres between them and customers.
The rules will not apply to children under the age of 13 or anyone who cannot wear one due to physical or mental incapacity.
Those who do not comply could face a €2,500 fine and a potential prison sentence.
Wearing a cloth face covering may help prevent people who do not know they have the virus from spreading it to others.
More advice can be found here