Ms Peters also said every store in the country will close early, at 8pm, on Wednesday night to restock essential products.
She assured Australians there will be plenty of products to come.
"We do not have a concern with the supply of our product," she said. "What we're seeing is a demand or spike in product at our stores."
She thanked Woolworths staff and said the company would maintain a no-violence policy.
"What I ask for is, as we saw in the Australian bushfires, we help one another, look out for the most vulnerable and make a real difference," she said.
"No matter how frustrating the customer experience can be... nobody should come to work to be physically assaulted, hurt or abused."
The Shop, Distributive and Allied Employees Association (SDA) Union called for calm during shopping.
"Customers, check yourself before you check out," SDA National Secretary-Treasurer Gerard Dwyer said.
"Don't lose it over a loo roll."
Earlier the company dismissed reports that delivery services would be suspended nationwide.
It tweeted saying it was only temporarily pausing services in parts of Victoria, where state Premier Dan Andrews announced a State Health Emergency this morning.
Woolworths' move to offer dedicated shopping time for the elderly and people with disability was prompted by the unprecedented demand in supermarkets over the past week, which has seen many elderly and vulnerable people missing out on vital items they may need when they shop.
Since the announcement, #Woolworths has been trending on Twitter.
Across the country, people have praised the supermarket giant.
While the feedback has mostly been positive, some on social media said the time frame was inconvenient for society's most vulnerable because it meant travelling during peak-hour traffic.
People with Disability Australia CEO Jeff Smith agreed that it was a good move by the supermarket giant, but more could be done.
“It is good to see major supermarkets making limited moves to support people with disability,” he said.
“However, we are very disappointed that deliveries have been suspended, and that they have not moved earlier to ensure people with disability can get the essential supplies we need.
Mr Smith said many people with disability did not have a concession card.
"(They) will not be eligible for this particular shopping hour, so we call on the supermarkets to extend this facility to include all of us," he said.
“People with disability must not be left stranded by preparations to deal with this ongoing public health emergency.”
From Tuesday, 17 March, Woolworths Supermarkets will open to all customers from 8am.
Access to the store before this time will require a relevant Government issued concession card.
Woolworths says it's reserving one hour for elderly customers amid COVID-19 outbreak
Meanwhile, Coles has announced it will hire 5,000 new casual workers to restock empty shelves.
Coles supermarkets will also shut from 8pm to make sure shelves can be filled and cleaned for the following day.
In addition, ‘click and collect’ online orders will be largely suspended in order “to dedicate vans to … the most vulnerable and those isolated”.
“We sincerely apologise for the inconvenience that this will cause and a further announcement about this will be made in the coming days,” Coles CEO Steven Cain said.
The measures will come into effect on Wednesday.