There is no official word on the cause of death. The prince had had a number of surgeries in recent years.
He was the kingdom's foreign minister for 40 years, before retiring in April. Arab League chief Nabil al-Arabi said the world had lost a "noble" diplomat.
Analysts say he was widely respected, and navigated through decades of turbulence in the Middle East.
He was regarded as the public face and voice of a country that preferred to conduct its diplomacy discreetly.
"Prince Saud al Faisal was a man of great humanity, compassion and wisdom," former British Prime Minister Tony Blair said in a statement. "He worked tirelessly for peace."
Saudi Foreign Ministry spokesman Osama Nugali said: "The eye tears, the heart saddens."
The son of King Faisal, Prince Saud was born in 1940, and was among the first generation to receive both a traditional and a Western education.
Prince Saud studied economics at Princeton University in the US in the 1960s.
In 1970, he became deputy governor of the former state-owned natural resources company, Petromin, and the following year was appointed deputy minister of petroleum and mineral resources.
He was was appointed foreign minister in 1975.
Saudi Arabia's Prince Saud al-Faisal - who was the world's longest-serving foreign minister - has died aged 75.