The event, which was due to see the great grandchildren of the former South African president quiz their grandmother, Zindzi in a family-friendly talk at 5pm, has been postponed until tomorrow morning.
The delay comes as new figures today showed that passport control queues at Heathrow Airport reached two and a half hours last month.
A statement issued by the Edinburgh International Book Festival said: "The Mandela family were stopped at Heathrow security & missed their flight so won't make the event at 5pm. The event will now take place tomorrow at 10.15am. A full refund will be given to anyone who can no longer make it."
The event, ‘My Grandad, Mandela’, is set to see Mandela’s great grandchildren, Zazi and Ziwelene, aged six and seven, ask their grandmother a series of 15 questions about the leader in an talk which the festival said would see them “find out how they can continue his legacy in the world today”.
It is believed that the delay at Heathrow after the family landed from South Africa resulted in the family missing their connecting flight to Edinburgh.