Prince Mansour bin Muqrin, the deputy governor of Asir province, was travelling with several officials when the helicopter crashed, Al-Ikhbariya news channel said.
The cause of the crash is unknown.
Saudi Arabia said it intercepted a ballistic missile, fired from Yemen, near Riyadh airport the day before.
Also this weekend, an anti-corruption purge targeted dozens of people, including 11 princes and four ministers, in a move seen to cement the power of the heir to the throne.
The anti-corruption body is led by Crown Prince Mohammed bin Salman.
Prince Mansour bin Muqrin, who died in the crash, is the son of another former crown prince.
The fate of the other occupants of the helicopter remains unclear, but Saudi news outlet Okaz said that unconfirmed reports suggested there were no survivors.
The group had been carrying out an aerial inspection of the region at the time, it said.