Foodstuffs NZ head of corporate affairs Antoinette Laird said some stores had experienced "capacity issues due to the significant increase in customer demand for online".
"While they are doing their best to meet all customers' needs, on occasion, they have been left with no option but to cancel an order – this has usually been because the number of orders has exceeded the team's ability to pick and deliver.
"Teams in-store are doing their very best to ramp up and meet customers' new online needs, but we ask customers to bear with us as the teams settle into this 'new normal' of needing to provide a much larger number of online and click and collect orders."
The woman said she had her order cancelled this morning without any notice.
"As a parent in isolation New World cancels our orders and it was due at 9.30am ... [New World] hasn't contacted anyone. I rang them to say what's the deal and they said their system is down nationwide."
The woman said it took them three hours to place their order yesterday morning.
She was unimpressed to learn they were now left with nothing.
"We called them and they said they tried to call us but kept saying it's good news you're getting your money back. People rely on these slots they booked for deliveries and they said all orders are cancelled - not ideal in these times.
"We could have had someone else get everything for us but we're now stuck.
Laird apologised to those who had their order cancelled.
"It is not something the teams do lightly."
Laird encouraged customers to shop as they normally would as it was "the best way to ensure we can meet everyone's needs".
Meanwhile, Laird was asking shoppers to be kind staff going into its supermarkets after reports of some frontline staff getting abused.
One shopper at New World Kumeu said she witnessed customers giving staff a "really hard time" about products being out of stock or having limits on them.
"The checkout operator said that they're getting abused frequently at the moment by frustrated customers," the woman posted online.
"We may all need to take a deep breath from time to time, everyone is doing their best," Laird said.
"The arrival of Covid-19 has absolutely put pressure on our supply chain, but it's robust and we're coping well under the circumstances.
"The best thing people can do to help us get through this to shop normally and resist the temptation to stock up, this is where the pressure comes."