Bin Laden had his citizenship removed on February 22 by royal decree, the Saudi newspaper said, quoting the kingdom's interior ministry.
It did not give a reason for the decision.
The US on Thursday offered a $1 million (0.9 million euros) reward for information on Hamza bin Laden, who it sees as an emerging face of extremism.
Al-Qaeda's September 11, 2001 attacks on the United States killed some 3,000 people and sparked the US intervention in Afghanistan.
A US Department of State reward poster for Hamza bin Laden. Source: Rewards For Justice
Bin Laden, who according to Washington is around 30, has threatened attacks against the US to avenge the 2011 killing of his father -- who was living in hiding in the Pakistani garrison town of Abbottabad -- by US special forces.
"Since at least August 2015, he has released audio and video messages on the Internet calling on his followers to launch attacks against the United States and its Western allies," the US State Department said in a statement on Thursday.
The 15th of Osama bin Laden's 20 children and a son of his third wife, Hamza has been groomed to follow in his father's footsteps since childhood.
At his father's side in Afghanistan before the 9/11 attacks, Hamza learnt how to handle weapons, and ranted in his thin voice against Americans, Jews and "Crusaders" in videos uploaded online.
On the eve of the attacks on the World Trade Center and the Pentagon, Hamza was separated from his father, whom he was never to see again.
The location of bin Laden, sometimes dubbed the "crown prince of jihad," has been the subject of speculation for years with reports of him living in Pakistan, Afghanistan, Syria and Iran.
He is believed to have spent years along with his mother in Iran, despite Al-Qaeda's strident denunciations of the Shiite branch of Islam that dominates the country.
Observers say that the clerical regime in Tehran kept him under house arrest as a way to maintain pressure on rival Saudi Arabia as well as on Al-Qaeda, dissuading the Sunni militants from attacking Iran.
In 2015, bin Laden released an audio message urging jihadists in Syria to unite, claiming that the fight in the war-torn country would pave the way to "liberating Palestine".
And in a message a year later, repeating one of his father's central messages, he urged the overthrow of Saudi Arabia's leadership.
One of Hamza bin Laden's half-brothers told The Guardian last year that Hamza married the daughter of Mohammed Atta, the lead hijacker in the September 11, 2001 attacks.
