There were no immediate reports of casualties at the refinery, which is one of the largest in Italy.
Fire and emergency services were scrambled to the refinery in the town of Nazaro de Burgondi, where the fire broke out at 4 p.m. (local time)
Plumes of black smoke could be seen billowing above the surrounding area, which eyewitnesses filmed and posted to social media.
"The fire is currently being extinguished," Eni said in a press statement.
"No damage to people has been registered.
The causes of the fire are being determined," the statement added.
Workers were ordered into bunkers at the plant.
In a message on its Facebook page, the local council advised residents to stay in their homes or to seek shelter in the nearest closed location.
Roads around the refinery were closed to traffic and police and staff from Italy's civil protection agency were deployed to the area.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)