Prince Nayef, 79, will be buried Sunday, leaving the country temporarily without a successor to his 88-year-old brother, King Abdallah, Voice of America said.
"The news of Prince Nayef bin Abdul-Aziz's death was shocking to everyone in the kingdom and to the royal family," Saudi Foreign Ministry spokesman Osama Nogali told CNN. "We still don't know the reason behind his death."
U.S. President Barack Obama, in a statement released by the White House, lauded the prince for his decades of work on behalf of Saudi Arabia's and the region's security.
"Under his leadership, the United States and Saudi Arabia developed a strong and effective partnership in the fight against terrorism, one that has saved countless American and Saudi lives," Obama said. "Crown Prince Nayef also strongly supported the broader partnership between our two countries begun by his late father, King Abdul al-Aziz al-Saud, and President [Franklin] Roosevelt in their historic meeting in 1945. On behalf of the American people, I would like to offer my deepest condolences to King Abdallah, the royal family and the people of Saudi Arabia."
VOA said the prince had recently been in Europe for treatment of an undisclosed health matter.
Nayef is the second crown prince that King Abdallah has outlived. He became first in line to the throne only in October while serving as interior minister.
The prince had been considered a reliable ally of the west in its campaign against al-Qaida, which had the overthrow of the Saudi royal family among its top priorities. He was also considered a staunch political and social conservative who took a dim view of liberalizing the kingdom, Britain's Sky News reported.
The passing of Nayef means Abdallah must select another successor from a long list of relatives.