Port officials blamed the French authorities for providing insufficient staff to check passports before passengers and vehicles could board ferries at one of their busiest periods of the year with the start of the English school summer holidays.
Travellers said the delays were the worst they had experienced, with one lorry driver waiting more than 15 hours due to the problems with border control staffing.
The Road Haulage Association, whose members include several Scottish seafood firms, said some goods would have to be destroyed because of the hold-ups.
Association spokesperson Kate Gibbs said: "We are concerned for the welfare of all the hauliers that are held up in these latest queues at Dover and the knock-on effects for the cross-Channel supply chain.
"However, for those carrying perishable goods, such as fresh meat and live seafood, the problem is even greater.
"The longer the goods stay on the back of a truck, the shorter the shelf life when they finally reach the customer.
"It is inevitable that in some cases, the goods will have to be destroyed."
A spokesperson for Logistics UK, which represents the haulage industry, said: “Dover is a critical route for Scottish exports, as well as all freight leaving the country, and therefore it will delay goods leaving Scotland for customers in the EU.
“However, there should be no impact on goods arriving in Scotland via Dover due to the fact there are no additional checks on freight import traffic.”
Holidaymakers booked on sailings from the Kent port reported being stuck in five-hour queues to complete border checks before they could check in for their ferry.
Vehicles including lorries, family camper vans and cars with bicycle racks queued through Dover to reach the port.
Passengers embarking on cross-Channel sailings from Dover must pass through French border checks before they can board a ferry.
The port said in a statement it had made “significant investment” to increase its capacity, and shared traffic volume forecasts “in granular detail with the French authorities”.
It said: “Regrettably, the PAF (police aux frontieres) resource has been insufficient and has fallen far short of what is required to ensure a smooth first weekend of the peak summer getaway period.
“Knowing we are now in a new world of post-Brexit and Covid checks, we worked to increase interim French border control booths by 50 per cent and have improved traffic systems in order to build in resilience and capacity in time for the summer."
The chief executive of the Port of Dover said it was “immensely frustrating” to be “let down” by poor resourcing at the French border.
One traveller took to social media, writing: "I'm booked onto 8am ferry from Dover and it's total gridlock. Moved 50 metres per hour. At this rate it'll be 34 hours before I get to the port.”
P&O Ferries told passengers: "There are currently queues in excess of four hours to reach the border controls.
"Our check-in remains free flowing and once you reach us, we will put you on the first available sailing.
"Please arrive prepared for a prolonged wait.”