The balloon was at 300m (1,000ft) when it caught fire and plunged into fields west of the ancient city.
At least two people, including the balloon's pilot, are reported to have jumped out of the balloon before it crashed.
Officials in Luxor say they have now banned all hot air balloon flights.
People were jumping out of the balloon from about the height of a seven-storey building
Witness Cherry Tohamy
The UK Foreign Office said that two British nationals and one British resident had died. One of them was said to have undergone five hours of surgery in an effort to save his life, but died of his injuries. Another Briton is in a stable condition in hospital.