Hamza, who is now in his late 20s, was named an official member of al-Qaeda in 2015 and is seen as a possible successor to his father.
Since then, he has called for attacks against western capitals.
The US State Department said it was notifying the international community that "Hamza bin Laden is actively engaged in terrorism".
The official sanction blocks him from any business dealings with US companies or holding property on US soil.
Hamza is the son of the former al-Qaeda leader and Khairiah Sabar, one of Osama's wives who was captured during the 2011 raid on his father's Abbotabad compound in Pakistan.
Hamza was not in the compound with his parents during the raid, in which Osama Bin Laden was killed.
Ayman al-Zawahiri, an eye surgeon who helped found the Egyptian Islamic Jihad militant group, took over leadership of al-Qaeda after his death.
In August, Professor Fawaz Gerges, an expert on Middle East politics, told BBC Radio 4 that Hamza was "the new face of al-Qaeda - he is charismatic, he is very popular with the rank and file".
"He was his father's favourite son - everyone, even for the last ten years, has been talking about Hamza succeeding his father."
In 2015, al-Qaeda released an audio message from Hamza, which called on followers in Kabul, Baghdad and Gaza to wage jihad, or holy war, on Washington, London, Paris and Tel Aviv.
He now joins his half-brother Saad on the US sanctions list as a "specially designated global terrorist" -  someone who threatens national security or the safety of US citizens.
The US State Department said the sanction was a "powerful tool."
Individuals and groups sanctioned under the programme range from offshoots of the Irish Republican Army (IRA) to the so-called Islamic State, among thousands of others.

Calen Gaze, 17, from Gloucester, was found guilty of wounding with intent to cause grievous bodily harm, at Gloucester Crown Court last October.
His 13-year-old victim suffered a shattered cheekbone and eye socket.
Gaze, who was 15 at the time of the attack in 2015, was originally sentenced to 240 hours of unpaid work.
The Court of Appeal in London heard Gaze, from Ashcroft Close, Matson, knocked the boy down by punching him in the face, and then stamped on his head "numerous times" at a park in the Abbeymead area of the city.
The scuffle began after a row over a rugby ball between two groups of boys at a playing field in Hucclecote, the court was told.
The victim had to have emergency surgery, and titanium mesh and plates were inserted to support his eye and repair fractures to his cheekbone.
He was advised by doctors not to take part in contact sport as the mesh could sever his retina.
Lawyers acting for the Attorney General Jeremy Wright QC said Gaze's initial sentence was too light for such a serious attack.
Paul Jarvis told the court that, had Gaze been an adult, a sentence of about 12 years could have been expected.
In sentencing Gaze to four years in a young offenders' institution, Lord Justice Fulford said the offence was "so serious that neither a fine, nor a community penalty, can be justified".
The appeal court also lifted a ban on the media naming Gaze, despite him being under the age of 18.

The Championship Rams turned a one-goal half-time deficit into a 2-1 victory to book a place in the fourth round.
McClaren told BBC Radio Derby: "We told them to keep their composure We were causing them problems and controlling the game.
"How the players kept their composure and came back, credit to them."
Darren Bent and Tom Ince scored goals three minutes apart in response to Matt Phillips putting the hosts ahead in the first half.
And McClaren was keen to point out the contribution of a massive following from Derby.
"I had heard 6,000 were coming along and they were going to fill behind the goal," continued McClaren.
"We said to the players that it's a cup tie and there's 6,000 fans coming to watch, so there's a reason why we've got to fight, we've got to react and come back.
"I'm so pleased for the players, I'm so pleased for the fans and very proud of them."
Hamza bin Laden, a son of Osama bin Laden, has been officially designated a global terrorist by the United States.
[NEXT_CONCEPT]
A teenager who stamped on a boy's face has been given a four-year sentence by appeal court judges after his previous sentence was deemed "unduly lenient".
[NEXT_CONCEPT]
Manager Steve McClaren praised Derby County's control as they came from behind to knock Premier League West Brom out of the FA Cup.