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.
Hamza, who is in his mid-twenties, has become active as an Al-Qaeda propagandist since his father's death in 2011.
The designation by the State Department imposes sanctions on foreign persons determined to have committed, or pose a serious risk of committing, acts of terrorism that threaten the security of US nationals or the national security, foreign policy, or economy of the United States.
As a result of this designation, all property subject to US jurisdiction in which Hamza has any interest is blocked and US persons are generally prohibited from engaging in any transactions with him.
The State Department said on July 9, 2016, al-Qaeda issued another audio message from Hamza bin Laden threatening revenge against the United States and warned Americans they would be targeted in the United States and abroad.
"In 2015, (Hamza) bin Laden called for lone offender attacks against US, French and Israeli interests in Washington, D.C.; Paris, France; and Tel Aviv, Israel," it said.
"Additionally, in 2016, (Hamza) bin Laden called on Saudi Arabian-based tribes to unite with al-Qaeda's affiliate in Yemen to wage war against the Kingdom of Saudi Arabia," the State Department said.
Simultaneously, the State Department also designated Ibrahim al-Banna, a senior member of Al-Qaeda in Arabian Peninsula, as a Specially Designated Global Terrorist.
Al-Banna has served as AQAP security chief and provided military and security guidance to AQAP leadership.
A 2010 edition of AQAP’s English online magazine, Inspire, contained an article by al-Banna describing the 9/11 attack as virtuous and threatened to target Americans both domestically and elsewhere, in response to US actions overseas, the State Department said.
Before joining AQAP, al-Banna was a leader of the Egyptian Islamic Jihad in Yemen from 1996 to 1998 and subsequently was in-charge of the training and intelligence sectors for the group.
"Al-Banna is also subject to a US government reward of up to USD 5 million," the State Department said.