French border controls have been blamed for the delays of up to six hours.
The Port of Dover has declared a “critical incident” because of long queues leading to the ferry terminal.
Boss Doug Bannister told BBC Radio Kent the port had been “badly let down” by the French border controls.
He said they were “insufficiently resourced” in France and working slower than normal, leading to significant congestion.
National Highways said the weekend was expected to be one of the busiest periods of the year for holidaymakers.
The Port has accused the French authorities of ruining the summer getaway for thousands of families.
Holidaymakers booked on sailings from Dover have reported being stuck in five-hour queues to complete border checks before they can check in for their 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”.