The casualties were rushed to hospital but there is no update on their condition, Luxor governor Mahmoud Badr confirmed.
The health ministry identified the dead person as a 36-year-old woman.
According to a security source that spoke to Ahram Arabic website, the hot-air balloon crashed due to strong wind.
All of those involved in the accident are believed to be foreign tourists.
In 2013, a hot air balloon caught fire in mid-flight over Luxor, killing 19 tourists.
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Those on board the flight included a number of foreign nationals from South Africa, Argentina and Spain, along with Egyptian tourists.
The balloon, carrying tourists from different nationalities and Egyptians, crashed to the west of the city of Luxor, state-run news agency MENA reported.
Hot air balloon rides were temporarily suspended in Egypt in 2016 after a crash landing led to the injuries of 22 Chinese tourists.
Hot air balloon crashes have occurred in the region before.