The rules also apply to shopping centres and hairdressers.
People could be fined 2,500 euro for not wearing a mask in shops and shopping centres from today.
The new rules also apply to indoor retail settings including hairdressers, libraries and cinemas.
Children under 13 and people with a disability or physical or mental illness are exempt.
These people in Dublin shared what they think of the new regulations:
Retail Ireland director Arnold Dillon expects most people to comply - and that any disputes will be rare.
''What we have now with the new rules is a very sensible approach, retailers are mandated to actively encourage the use of masks'', he said.
''But the ultimate authority is enforced by the gardai and what that will do is give retail workers the flexibility to encourage the use, but also be able to avoid potentially dangerous situations''.