No deaths have been reported in connection with the incident.
"The Mina Al-Ahmadi refinery was targeted by a drone attack early this morning, resulting in fires in several operational units," the state-run Kuna news agency reported.
During the night, the military announced that the country's air defenses were trying to stop missiles and drones heading toward its territory.
The refinery, which was shelled by Iran earlier in the war, is one of the largest refineries in the Middle East, with a capacity to process around 730,000 barrels of oil per day.
