They're anxious over backlash from customers.
The Health Minister says regulations are being drawn up to make face masks mandatory in shops.
Customers now have to wear face coverings in all stores.
But it's unclear how it will be policed and what penalties will be enforced.
Minister Stephen Donnelly says they are working on it:
Paul Lynam from The King Oak store in Tullamore agrees with the wearing of face masks, but is worried about how the measure will be policed: