The balloon carrying 21 people was flying at 300 metres (1,000 feet) when it caught fire, a security official said.
An employee at the company operating the balloon, Sky Cruise, said the pilot and one tourist survived by jumping out of the basket before it hit the ground. Both were taken to hospital.
Security services cordoned off the scene of the crash in Luxor's dense sugar cane fields, as police and residents inspected the charred remains of the balloon.
The balloon had been floating over the west bank of Luxor, one of Egypt's most renowned archaeological sites and home to the famous Valley of the Kings and the grand Temple of Hatshepsut, when it exploded.
French hot air ballon expert Philippe Buron-Pilatre de Rozier said the blast could have been caused by a leak after a spark caused by a lighter or a cigarette.
Another reason could be wear and tear due to poor maintenance or if the pilot is badly positioned, said Buron-Pilatre de Rozier, adding that hot air balloons such as the ones used in Egypt are generally 40 metres (130 feet) high and can carry up to 25 passengers.
There were contradictory reports over the death toll and the nationalities of those killed in the crash.
An Egyptian security official said 19 tourists had died including nine from Hong Kong, four from Japan, three Britons, two French tourists and one Hungarian.
The health ministry said 14 people had died, and four were missing. It said three people survived but were injured in the crash, including two Britons and one Egyptian.
British tour operator Thomas Cook said two Britons were killed and two hurt in the crash.
"We can confirm that two of our guests are in local hospitals, but tragically two of our guests have died in the hot air balloon incident in Luxor, Egypt this morning," Thomas Cook said in a statement.
The Japanese embassy in Cairo said it was trying to confirm the reports that Japanese nationals died in the accident.
The French embassy was also trying to ascertain whether French nationals had died in the crash, amid conflicting reports.
In Hong Kong, the general manager of a tour operator said nine Hong Kong people were feared dead.
"We believe that there is a high possibility that nine of our customers have died," Raymond Ng of travel agency Kuoni which organised the Hong Kongers' tour told a news conference.
The five women and four men were aged between 33 and 62, Ng said.
Their relatives were to fly to Cairo later on Tuesday via Qatar, accompanied by three staff from Kuoni, he added.
The nine were from a group of 15 Hong Kongers who had left for Egypt on February 22. Ng said that according to local employees, the balloon caught fire about an hour after it had set off, plummeting to the ground two minutes later.
"This is terrible, just terrible," the Sky Cruise employee told AFP by telephone, declining to give her name. "We don't yet know what happened exactly or what went wrong," she said.
In 2009, 13 foreign tourists were injured when their hot air balloon hit a phone mast and crashed at Luxor. Sources at the time said the balloon was overcrowded.
The crash comes amid widespread anger over safety standards in Egypt following several deadly transport and construction accidents.