Passengers at Heathrow face 12-hour long queues when border officials join next Wednesday's public sector strike over pensions, according to the airport's operator.
BAA has warned the world's busiest airport will be crippled by "gridlock" and that arriving planes may have to be diverted to other countries.
In a letter to airlines, Heathrow's chief operating officer Norman Boivin said delays at immigration are likely to be so long that passengers may not be able to be safely accommodated within terminals and would need to be held on arriving aircraft.
"This in turn would quickly create gridlock at the airport with no available aircraft parking stands, mass cancellations or departing aircraft and diversions outside the UK for arriving aircraft," he said.
"Modelling of the impacts of strike action on passenger flows at Heathrow show that there are likely to be very long delays of up to 12 hours to arriving passengers."
Immigration staff are set to walk out on November 30 as an expected 2.6 million public sector workers strike over planned changes to their pensions.
Unions have said that plans to make their members work longer and contribute more are unfair.
David Cameron has branded the strike "irresponsible" and the Treasury has claimed the day of action will cost the economy more than £500m.
The Home Office plans to staff border controls at airports with non-unionised civil servants from across Whitehall. According to the Guardian the UK Border Agency plans to fly home embassy staff from abroad to man the border.Suggest a correction