The prince, who had been ill for a long time, died early Saturday at a hospital in New York, CNN reported. The Saudi government said his funeral will be held Tuesday.
"King Abdullah bin Abdulaziz Al-Saud mourns the death of his brother and his Crown Prince," a statement said.
Sultan was defense minister for decades. He played a key role in the decision to allow U.S. troops into Saudi Arabia during Operation Desert Storm, the first Gulf War.
Foreign leaders sent messages of condolence to Saudi Arabia.
"He had many friends in this country, and we have all benefited from his wisdom and expertise in international affairs over his long years of service to the Kingdom," British Prime Minister David Cameron said. "I know that the ties between our two countries will remain strong and that we will continue to work together for peace, prosperity and justice in the world."
No announcement has been made on the succession to the throne, CNN said. One likely candidate to replace Sultan as heir is Prince Nayef bin Abdul Aziz, 78, the interior minister and another half-brother of the king.
Abdullah created a Council of Allegiance, consisting of members of the royal family, in 2007 that could consult on an heir. But he also named Nayef second deputy prime minister in 2009 and has not said if he will involve the council.
Sultan was believed to have been born in either 1924, the same year as King Abdullah, or in 1928. He had been suffering for several years from medical problems.