The officials say today's incident was caused by strong winds that forced the balloon off its course above the city's pharaonic temples and tombs.
There were no details immediately on the nationalities of the victims. The officials spoke on condition of anonymity under regulations.
Hot air balloon incidents have occurred in the past over ancient Luxor.
In 2013, 19 foreign tourists were killed when their balloon caught fire. In 2016, Egypt temporarily halted balloon flights after 22 Chinese tourists suffered minor injuries in a crash landing of their hot air balloon.