The Government has announced that face coverings must now be worn in all shops, retail settings and shopping centres.
It said the strong advice is for people to start obeying the guidance immediately, but said regulations will take some time to draft.
Regulations to enforce the compulsory wearing of face coverings on public transport came into effect this week.
Following a Cabinet meeting at Dublin Castle this evening, Taoiseach Micheál Martin announced the new measures after confirming that Ireland will not progress to Phase 4 of lifting coronavirus restrictions.
Cabinet agreed that current health measures on Covid-19 should remain in place until 10 August.
Mr Martin announced that retail staff will be required to wear face coverings unless there is a partition in place or a space of two metres between them and customers.
Retail Ireland said that when it comes to enforcement of the measures, it is "crucial that it does not fall to retail staff to ensure compliance".
The organisation's director, Arnold Dillon, said that enforcement of the measures should be left to the appropriate authorities and retail staff should not be exposed to "the potential disputes and discord that might arise".
Mr Dillon said: "It is vital that provision is made for some flexibility when it comes to the application of any new rules for retail staff.
"Retailers have made enormous efforts to protect staff, who are working all day long in retail settings, including putting in place screens around cash registers and counters. This needs to be reflected in the approach."
Earlier, the Mandate trade union called for compulsory face coverings in shops and supermarkets to protect retail workers from the dangers of contracting Covid-19.
The union, which represents 35,000 retail and bar workers, called on the Government to engage urgently with the union to develop protocols for implementing the obligatory wearing of face coverings in retail outlets.
Additional reporting Ingrid Miley