According to Skynews Arabia, the attack was reported on Wednesday morning.
Two Iraqi employees of the company were injured in the attack, the report said.
Reuters reported that oil workers said they heard 3 explosions in Basra.
Exxon Mobil has announced that it plans to evacuate 20 foreign staff members from Basra after the incident.
Meanwhile, a rocket landed near an Iraqi military base hosting US forces in the northern city of Mosul late on Tuesday, an Iraqi military statement said, the second such incident in two days.
The statement gave no immediate reports of casualties. It said the rocket fired was a short-range Katyusha missile.
Mosul’s military commander said the rocket landed in an open space causing no casualties or damage. He said it was fired from west Mosul, across the Tigris river, and was a “locally made” rocket, without elaborating.
On Monday, three rockets hit a base that hosts US forces north of Baghdad.