Ain al-Asad base is home to about 1,500 US and coalition troops.
US soldiers say the attack destroyed several facilities, but that they had a warning. They had hours to prepare and moved personnel, weaponry and aircraft to fortified bunkers.
No one was killed or injured in the attack.
Iran targeted al-Asad base in response to the killing of Iranian General Qassem Soleimani in a US drone attack in Baghdad on January 3.