Roger Burnley told the Press Association that anything disrupting established food supply chains, currently governed by EU customs arrangements, would have “significant consequences”.
“What would be scary is the prospect of any hold up at the border. Any prospect of a hold up - that includes the southern Ireland border - would have very significant consequences.
“You’d be eating into the life of products with all sorts of implications for waste, for freshness, for quality,” he said.
Businesses such as Airbus and BMW have become increasingly vocal in recent weeks over the impact of Brexit, calling for urgent clarity as the Government continues to dither over its position.
Mike Coupe, the chief executive of Sainsbury’s, which is merging with Asda, has also issued a similar warning regarding the impact of customs delays.
Tesco boss Dave Lewis has warned that tariffs, which could be levied in the event of a no-deal Brexit, would see everyday prices rise.
The British Retail Consortium and a host of other organisations have also said that food prices could rocket if the Government botches Britain’s exit from the bloc in March 2019.
Mr Burnley pointed to Ireland - whose border has emerged as a bone of contention in the Brexit debate - as a key flashpoint for Walmart-owned Asda.
“Like any business, we all want certainty and to know what is happening, but... we want hassle-free frictionless borders, it’s number one on my list.
“A lot of our meat comes from Ireland, the prospect of a border control that slowed things down there would be quite dramatic on that part of our business.”
The direct intervention into the Brexit debate comes at a critical time for Prime Minister Theresa May, who is attempting to hold together a warring Cabinet that does not agree on what kind of Brexit Britain should pursue.
The Conservative Party has promised the country the “exact same benefits” of single market membership, while in the same breath pledging to leave it alongside the customs union.
An internal Government study has shown that the UK could be hit with food shortages within weeks of leaving the EU if a Brexit deal is not reached.
Asked whether the Government would reach a satisfactory deal with the EU before Brexit day, Mr Burnley said: “I’m hopeful.”