Prince Abdulaziz bin Fahd, a son of the late king Fahd, was rumoured to have been killed in custody or while resisting arrest amid the crackdown at the weekend.
The hashtag "death of Prince Abdulaziz bin Fahd" has since featured on social media, fuelling fevered speculation online.
"There is no truth whatsoever to rumours circulating in media concerning Prince Abdulaziz bin Fahd," an information ministry spokesman said in a statement.
"Prince Abdulaziz is alive and well," he added.
The prince could not be independently reached for comment.
It was the biggest purge of the kingdom's elite in modern Saudi history.
Separately, on Sunday another prince, Mansour bin Moqren, was reported killed in a helicopter crash near the kingdom's southern border with Yemen. Authorities did not reveal the cause of the crash.
With the purge, which analysts describe as a bold but risky power play, Prince Mohammed has centralised power to a degree that is unprecedented in recent Saudi history.
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