The target was the enclave of Ain al-Assad, in the western province of Al-Anbar.
The shells fell in the vicinity of the facility with no information so far on casualties or material damage.
According to the report of the Shafaq news site, the anti-aircraft system was activated during the attack.
Last Tuesday, the soldiers of the same base neutralized two drones loaded with explosives that were heading towards the enclave.
Such attacks come amid growing anti-U.S. feeling coinciding with the second anniversary of the assassination in Baghdad by U.S. aircraft of Iranian General Qassem Soleimani.
Last July, Baghdad and Washington agreed to end the presence of US combat forces in the country, although some 2,500 military personnel will remain as advisors and trainers.
But the Iraqi Resistance considers this remnant of forces as an occupier and aspires to get them out of the country at any cost.
The Sayed al-Shuhada brigades in Iraq announced today that they will continue their attacks against US troops until their total withdrawal.
The spokesman of the group belonging to the Popular Mobilization Units (al Hashd al Shaabi), Kazem Al-Fartousi, declared that Washington must be serious in its commitment to pull its military out the country.
In any case, he added, hostility against U.S. forces is a natural outcome against the insistence on remaining in the territory.