Richard Walker, managing director of the supermarket chain, said there was no need for shoppers to panic-buy, with the retailer reporting "no supply issues" despite the outbreak.
The comments come as the supermarket revealed it has cut 29% of its yearly plastic usage after a series of sustainability pledges in 2018.
Mr Walker said shoppers were turning to frozen food in a bid to stockpile in case of self-isolation but warned that panic-buying could harm more vulnerable customers.
He said: "Sales are definitely ahead of forecasts for the past week.
"People are choosing to stock up on frozen and our deliveries are above expectations as well.
"We've had no problems with supply or stock whatsoever, although obviously demand has been high.
"I think customers also have a responsibility to shop responsibly as not everyone can afford to stockpile.
"It's important we all work together."
Trade publication The Grocer reported that a supermarket boss called on the Government to remove the 5p bag plastic charge following the virus outbreak, but Mr Walker said he believed there was no need for the change.
Mr Walker has spearheaded efforts by the retailer to cut down on plastic usage, with the chain removing 3,794 tonnes of plastic from its stores.
It revealed the plastic reduction two years after the retailer laid out plans which will see it remove plastics from all own-label product packaging
by the end of 2023.
Iceland said 74 of its frozen meal lines have been moved from non-recyclable black plastic and into paperboard-based trays.
It said it has also made "significant progress" in addressing other difficult to recycle plastics, including PVC and polystyrene.
Iceland has engaged almost 100 own label suppliers to establish working groups and set out frameworks for plastic removal
Branded suppliers have also been encouraged to take a collaborative approach on plastic packaging reduction, it said.
A series of trials have been launched to support its commitment, including its first plastic bag free store, the offer of a reduced plastic Christmas range, and installation of reverse vending machines in stores.
Store operations have also seen trials to reduce Iceland's carbon footprint, such as the development of reusable paper carrier bags.
Mr Walker added: "We opened our first plastic carrier bag-free shop in Hackney recently and have now rolled that out to 50 other stores.
"The paper bags are now in all stores too."
However, last year the company also ended two trials, to replace plastic packaging on bananas with paper hoops and to launch its first plastic-free greengrocer, after disappointing results.