The Justice Minister said Gardaí will be called as a last resort if people refuse to wear masks inside shops or shopping centres.
Face coverings will be mandatory in retail settings from Monday.
The Government hopes law enforcement will only be needed in a small number of cases, as has happened with rules around masks on public transport.
Minister Helen McEntee expects retail workers will engage with customers not wearing a mask.
Minister McEntee said: "The retail outlet or the shopkeeper would go to extents to show that and put up perhaps signage to say that masks need to be worn on the premises.
"Secondly if a person enters without one or remains inside the premise without it that there would be engagement between them and retail, either the owner or the person working in the shop.
"And then as a last resort, An Garda Síochána could potentially be called."
General secretary of Mandate Trade Union John Douglas says the enforcement of the measure should only take place at the entrance.
Mr Douglas said: "You have your gloves, your plastic gloves, and just extend that by saying: 'Look there's a box of masks here would you mind putting one on while you're in our shop.'
"And if someone point-blank refuses for whatever reason then they just have to refuse entrance and say: 'Sorry we can't let you in'.
"I think that resolves it because our members certainly won't be chasing around supermarkets or department stores asking people to leave."
Yesterday, Minister for Health Stephen Donnelly said it was unlikely the Gardaí would be necessary to enforce the new measures as members of the public are already complying with the regulations.
Minister Donnelly said Gardaí enforcing the regulation would be "the last port of call".
The vast majority of people are already wearing masks in shops, he said.
“Inevitably people will forget, but we have got to build it (wearing masks) into our habits.”