Prince Muhammad, who was born in Riyadh in 1934, was emir of the al-Baha region from 1987 to 2010.
The royal court said funeral prayers will be recited after sunset prayers Monday at a mosque in Riyadh, the Saudi Gazette reported.
The statement made no mention of a cause or location of the prince's death.
Muhammad was the third son of King Saud, serving in a number of positions, including minister of defense and aviation, before his father was deposed in a power struggle with his half-brother, Faisal, in 1964.
Married to one of King Faisal's daughters, he pledged fealty to the new king and went on to hold a number of other important positions in the kingdom.
Megyn Kelly: Santa Claus and Jesus are both white men
Wisconsin business offering 'therapeutic cuddling' forced to close