The CEOs of Asda, Iceland, Marks & Spencer, Sainsbury's, Tesco and Co-op said that "urgent intervention" was needed to address the current situation before new procedures are enforced when the "grace period" for simplified trade controls expires on March 31.
In a letter to the chancellor of the Duchy of Lancaster, Michael Gove, on Tuesday, the supermarket chiefs said: "The current proposals, increased bureaucracy and increased certification in such a short timescale, are unworkable."
Shortages of fresh fruit, vegetables and meat have been witnessed by customers in some supermarkets in Northern Ireland this week due to additional red tape imposed by the UK's post-Brexit trade deal with the EU.
Under the Northern Ireland Protocol, which took effect on January 1, businesses sending goods from England, Scotland and Wales to the region must comply with new regulations due to a customs border in the Irish Sea.
This allows Northern Ireland to remain in the EU's single market for goods, but means there are specific rules for British traders moving goods into the region, such as applying for export health certificates from official vets for animal products.
On Wednesday, MPs in the UK Parliament asked Gove about the potential food shortages and price rises faced by those in Northern Ireland, to which he responded by claiming that some of the problems have already been addressed.
"We will make it clear to the European Commission what the consequences would be if supermarkets are not in a position [after March 31] to carry on with the service they provide to Northern Ireland consumers," he said.
Gove also cited the head of the British Retail Consortium, Andrew Opie, who also signed the joint letter and who said that food supply chains were operating "as normal," according to Gove.