Sainsbury's warned on Monday that gaps will start to appear on shelves within days if transport ties are not quickly restored with mainland Europe.
The transport of freight across the English Channel has been disrupted after France suspended travel links with Britain to try to curb a new faster spreading strain of COVID-19.
"If nothing changes, we will start to see gaps over the coming days on lettuce, some salad leaves, cauliflowers, broccoli and citrus fruit – all of which are imported from the continent at this time of year," Sainsbury's said.
It urged the British and French governments to come to a mutually agreeable solution that prioritises the immediate passage of produce and any other food at the ports.
The UK was on Monday shut off from the rest of Europe after its closest allies cut transport ties due to fears about the new coronavirus strain, sowing chaos for families and companies just days before it exits the European Union's orbit.
France, Germany, Italy, the Netherlands, Austria, Switzerland, Ireland, Belgium, Israel and Canada were among those that shut off travel ties after Prime Minister Boris Johnson warned that a highly infectious new strain of the virus was a danger to the country.
Johnson will chair an emergency response meeting on Monday to discuss international travel, in particular the flow of freight in and out of Britain. EU officials are due to hold a meeting at 1000 GMT on coordinating their response.
As families and truck drivers tried to navigate the travel bans to get back home in time for Christmas, there were fears that fresh food supplies to and from Europe would be disrupted though supermarkets have enough to cope with festive demand for now.
"The closure of France to UK traffic, including accompanied freight poses difficulties for UK capacity to import and export key goods during the busy Christmas period," said Andrew Opie, director of food & sustainability at the British Retail Consortium.
"While goods can enter from France, few haulage firms will be willing to send trucks and drivers across to the UK without a guarantee they can return to the EU in a timely manner."
France shut its border to arrivals of people and trucks from the UK, closing off one of the most important trade arteries with mainland Europe, a step Transport Secretary Grant Shapps said was surprising.
"We're doing everything we can to get that restarted," Shapps told Sky. "They've said to us they want to restart the hauliers as quickly as possible."
Shapps said getting the bans lifted as swiftly as possible was his priority but that given British preparations for the end of the Brexit transition period, the country was well positioned for disruption.
The British government triggered plans it had for stacking up trucks in the southeast county of Kent - part of its plans for potential disruption when the United Kingdom exits the EU's orbit with - or without - a trade deal at 2300 GMT on 31 December.
Talks on a Brexit trade deal were due to continue on Monday.
Trucks are being stacked on the M20 motorway through Kent, heading towards the ports, which is closed to normal traffic. A nearby airport will also be used to hold freight.
The closure of the Channel Tunnel and ports for onward travel to France will affect the export of goods such as fish and shell fish from Scotland to Europe, and the import of food for British supermarkets if, as expected, European drivers refuse to travel.
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