The news channel Al-Ekhbariya announced the death of Prince Mansour bin Moqren, the deputy governor of Asir province and son of a former crown prince.
It did not reveal the cause of the crash or the fate of the other officials aboard the aircraft.
News of the crash comes as Saudi Arabia pursues a sweeping purge of the kingdom's upper ranks, with dozens of princes, ministers and a billionaire tycoon arrested as Crown Prince Mohammed bin Salman cements his hold on power.
Already viewed as the de facto ruler controlling all the major levers of government, from defence to the economy, Prince Mohammed is widely seen to be stamping out traces of internal dissent before a formal transfer of power from his 81-year-old father King Salman.
The crash also comes after Saudi Arabia on Saturday intercepted and destroyed a ballistic missile near Riyadh's international airport after it was fired from Yemen in an escalation of the kingdom's war against Iran-backed Huthi rebels.
The missile attack was the first aimed by the Shiite rebels at the heart of the Saudi capital, underscoring the growing threat posed by the raging conflict in Yemen.
The attack highlighted how the war in Yemen is increasingly spilling across the border since a Saudi-led coalition began its military intervention there in 2015.
Saudi Arabia led the intervention to prop up the government of President Abedrabbo Mansour Hadi after the Huthis forced him into exile.
Hoping for a quick victory against what it saw as Iranian expansionism in its back yard, Riyadh has so far been unable to remove the Huthis from Yemeni capital Sanaa.
