The Warehouse is advising customers on its website deliveries could take up to two weeks to arrive.
It said while it was trying to get through orders as quickly as possible, because of the high number of orders it was struggling to keep up.
"Orders with multiple items may be delivered as separate packages," The Warehouse said on its website.
"We're shipping orders as fast as we can, however some may be delayed and take between 10-14 days due to unprecedented demand."
It also could not guarantee click and collect orders would arrive quicker than home deliveries.
"This is because your order may be picked from our online fulfilment centres and sent to your collection store, the days in between is the time it takes to be picked and travel between stores," The Warehouse said.
"If you're a registered user, you can track your order here.
"If you place an order for Click & Collect we will notify you once your order is ready for collection."
If orders were placed prior to the lockdown period, it was either already on its way or would be with customers soon. There would be some exceptions, however, it said.
Constable Vincent Kahui joined in after much encouragement from the crowd.