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.
Hamza bin Laden, a son of Osama bin Laden, has been officially designated a global terrorist by the United States.