A fire and an explosion were heard before the balloon plunged onto fields west of Luxor, officials said.
Reporters at the scene said they counted at least eight bodies.
Luxor lies on the banks of the River Nile and is home to some of Egypt's most famous pharaonic-era ruins. It is a popular tourist destination.
A representative of eight firms that operate air balloon flights in Luxor said there had been a gas blast while the balloon was at 1,000 feet (300 metres).
"There were 20 passengers aboard. An explosion happened and 19 passengers died. One tourist and the pilot survived," Ahmed Aboud told Reuters news agency by telephone.
The British foreign office told the BBC it was making urgent enquiries with its colleagues in Egypt to confirm reports of British casualties.
