The department also blacklisted Al-Mujahidin Brigades (AMB), which it said had links to Hezbollah and had plotted a number of attacks against Israeli targets from a base in the Palestinian Territories.
"Today's designations seek to deny Nasrallah and AMB the resources to plan and carry out terrorist attacks," the State Department said in a statement. It said the actions denied Nasrallah and AMB access to the US financial system.
Later, the State Department announced it was offering up to $5 million each for information leading to the locations of Hamas leader Salih al-Aruri, Lebanese Hezbollah leaders Khalil Yusif Mahmoud Harb and Haytham Ali Tabatabaei under the agency's so-called Rewards for Justice Program.
The department said both Hamas and Hezbollah receive weapons, training and funding from Iran. Washington recently reimposed sanctions against Tehran after President Donald Trump withdrew the United States from a 2015 nuclear deal.
Earlier on Tuesday, Lebanese Prime Minister-designate Saad al-Hariri blamed Iran-backed Hezbollah for what he called "a big obstacle" in efforts to form a new government.
Hezbollah, a heavily armed Shi'ite Muslim group, has been pressing a demand for one of six Sunni Muslim lawmakers allied to it to get a cabinet position. Hariri has refused to give up one of the seats allocated for his mainly Sunni party.
Earlier on Tuesday, the US Treasury imposed sanctions on four people linked to Lebanon's Hezbollah who coordinate the Iran-backed group's activities in Iraq and designated the son of the group's leader as a global terrorist.
The U.S. Treasury added Shibl Muhsin Ubayd al-Zaydi, Yusuf Hashim, Adnan Hussein Kawtharani and Muhammad Abd-al-Hadi Farhat to its Specially Designated Global Terrorists list. Al-Zaydi is Iraqi and the others are Lebanese.