Retail Ireland say demand for non-perishable grocery products, hand gels and disinfectant wipes has increased in recent days.
They say retailers are working with suppliers to address any shortfalls that arise but that supply chains are well-placed to respond.
Musgraves - the group behind Super Valu and Centra - is building up its own-brand stock.
It is also reported that BWG, which owns the Spar brand, confirmed it was in ongoing contact with its 650 suppliers here.
TD Paul Murphy is calling on the government to legally cap prices on items like hand sanitiser.
The official advice to protect yourself from coronavirus is to wash your hands with soap and water or use an alcohol-based hand rub.
However, Mr Murphy of RISE said people have been telling him about steep increases in shop prices.
He said: "I've heard a number of stories of different pharmacies whereby hand sanitiser has more than doubled in price
"I think that it is unacceptable to have any sort of price-gouging going on at this time, taking advantage of people's real and legitimate fears and need for things like hand sanitisers, so I think we should follow the example of the French government which has placed price controls on hand sanitisers."