The injured included tourists from Spain, South Africa and Argentina.
The balloon was carrying both Egyptians and foreign tourists, with the nationality of the latter not yet having been disclosed.
Other balloons had taken off around the same time but landed safely, the officials added, speaking on condition of anonymity in line with regulations.
A message by Egypt's meteorological service warning of strong winds was sent out on Friday morning, especially for the Nile River delta region and northern Egypt.
Egypt's health ministry confirmed the death of a South African tourist and the number of those injured but did not give further details.
Hot air balloon companies in Luxor offer the tours usually starting at sunrise.
Since then, balloon rides have been monitored by cameras and banned from flying above 2,000 meters. The tragedy came four years after a hot air balloon crash injured 13 tourists seeking an aerial view of the city. The Valley of the Kings, which has dozens of ancient tombs, including that of King Tutankhamun, is located just outside the city.
In 2013, a hot air balloon caught fire in mid-flight over Luxor, killing 19 tourists.