Shoppers will notice the supply issues next January unless there is a "massive upgrade" in border facilities, the British Retail Consortium said.
The warning came after cabinet minister Michael Gove said that border checks are "inevitable" after the Brexit transition period ends on 31 December.
Officials said firms have enough time to prepare for the changes.
Border checks could quickly cause hold-ups at Channel ports of thousands of trucks, including those carrying fresh food, the BRC said.
The government will have to "move fast" to put in place the necessary border infrastructure and staff to cope with those checks by the end of the year, it said.
If it doesn't, "consumers in the UK will see significant disruption, particularly in the availability of fresh fruit and vegetables" the BRC's director of food and sustainability Andrew Opie warned.
"If you think this is going to hit us in January, that's our peak import season for things like fresh fruit and vegetables. Customers are really going to see the problems on supermarket shelves unless we get that infrastructure," he said.
"So, you've got enormous bureaucracy, enormous change, but crucially you've got a problem with the infrastructure at the key ports around the Channel, which currently really act as an extension of the motorway for our supply chain, where you will be holding thousands of vehicles every day."
"I don't know if you've been to Dover recently, but there isn't an enormous amount of room to hold that infrastructure," he added.
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