The State and Treasury departments said on Thursday that they had designated Hamza bin Laden a "global terrorist" who they said had "called for acts of terrorism in Western capitals".
Hamza, who is in his mid-20s, has become active as a member of al-Qaeda since his father's death at the hands of US special forces on May 2, 2011.
Egyptian deputy Ayman al-Zawahiri has since taken up the reins of the organisation, but Hamza has also issued audio messages to supporters. He was officially named an al-Qaeda member in 2015, the US state department said.
In August 2015, al-Qaeda released an audio message that it claimed had come from Hamza, in which he urged attacks on the US and its allies.
Osama bin Laden, who founded al-Qaeda and was the alleged mastermind of the September 11, 2001 attacks in the US, was killed by American special forces who raided his compound in Abbottabad, Pakistan.
Hamza was thought to be under house arrest in Iran at the time, and documents recovered from the compound indicated that aides had been trying to reunite him with his father.
According to letters found in the US raid on Osama's hideout in Pakistan, Hamza wrote to his Saudi-born father asking to be trained to follow him.
Bruce Riedel, an analyst with the Brookings Institution think-tank in Washington, has called Hamza the "new face for al-Qaeda" and "an articulate and dangerous enemy", Reuters news agency said.
The US also added Ibrahim al-Banna, a senior member of al-Qaeda in the Arabian Peninsula (AQAP) to the counterterrorism blacklist on Thursday.
Al-Banna, who was born in Egypt, has described al-Qaeda's 2001 attacks on New York and Washington as "virtuous", and threatened to target Americans in the United States and abroad, the state department said.
Before joining AQAP, he was a leader of Egyptian Islamic Jihad in Yemen, it said, adding that al-Banna threatened to target Americans abroad and urged Saudi tribes to unite with AQAP in Yemen to fight against Saudi Arabia.
Any property owned by the two men and subject to US jurisdiction may be frozen, and US citizens are prohibited from engaging in any transactions with them, the state department said.