However, shoppers are limited to three items per online shop and the offer is only available online until the end of Friday 24 June.
Customers can get three items for 3p when they use the code ICEPENNY at checkout when shopping on Iceland’s website.
Items that can be purchased for 1p include pantry staples such as granulated sugar, microwave rice, and cream crackers, as well as cleaning items like dishwashing soap and sponge scourers.
Fresh and frozen vegetables are also included in the deal, such as broccoli florets, cucumbers and a one-kilogram bag of onions, as well as children’s snacks such as yoghurt tubes.
Analysis by Which? found that most of the items on offer usually cost around £1 or slightly over.
Shopping online at Iceland requires customers to purchase a minimum spend of £25, with a £3 delivery fee. An order of more than £40 is eligible for free delivery.
Iceland was rated the best supermarket for online shopping in the Which? customer survey last year which asked more than 3,000 people to rate supermarkets in the UK.
In April, Iceland CEO Richard Walker said the supermarket was taking action to help shoppers cope with the cost of living crisis.
It reduced the minimum online spend for free deliveries and froze the prices of its £1 value range.
He wrote in a blog post: “Iceland will always stand up for its customers and we will continue to do everything we can to shield them from the huge and increasing pressures on their budgets that they are currently facing.”
The cost of living crisis has seen grocery inflation hit a 13-year high, jumping to 8.3 per cent in the four weeks to 12 June from seven per cent a month earlier.
Annual grocery bills are forecasted to increase by £380 this year, according to new data from Kantar.