The confirmation of Hamza's death has come more than a month after the US media reported that he was killed, citing the US intelligence officials.
The sanctions list subjected him to a travel ban, assets freeze and an arms embargo.
The US move comes nearly year and half after Hamza was officially announced by al-Qaeda chief Ayman al-Zawahiri as an official member of the group.
The US State Department had identified him as a "Specially Designated Global Terrorist" in January 2017.
Hamza bin Laden promised to continue the global militant group's fight against the United States.
Hamza, 29, has assumed a senior position within Al Qaeda and was aiming to avenge the death of his father, who was shot dead during a covert US military raid in Pakistan's Abbottabad seven years ago, Osama's half-brothers Ahmad and Hassan al-Attas were quoted as saying.