Prince Sultan, who had been fighting colon cancer since 2004, was operated on in July but no information has been made public since then. He was declared clinically dead a month ago, a diplomat told the AFP news agency.
The Al-Saud family has ruled Saudi Arabia ever since the kingdom was founded in 1932.
Under its rules of succession the throne passes in turn to the sons of its founder, Abdul Aziz.
All of them are now elderly.
King Abdullah, who has introduced timid reforms in the conservative kingdom, is in hospital in Riyadh after an operation on his back a week ago.
Sultan, who is half-brother to Abdullah, has been defence minister since 1962.
His half-brother, King Fahd, appointed him second deputy prime minister in 1982, making him second-in-line to the throne.
Prince Nayef, who is also a half-brother to Abdullah, is currently interior minister and was named second deputy prime minister in 2009.
Saudi Arabia, a key US ally, has seen demonstrations by its Shia-Muslim minority but no uprising on the scale of many of its neighbours.
Its rulers are anxious about the influence of Shia-majority Iran and it spearheaded a Gulf Cooperation Council intervention in Bahrain, a Shia-majority country ruled by a Sunni monarchy that has been rocked by protest this year.