The fire broke out in a major crude oil tank on Wednesday night before spreading to a second refinery on a road southwest of Arbil, capital of the autonomous Kurdistan region, the agency said.
The cause of the blaze was still unknown, it added.
Thick plumes of black smoke and balls of orange flame rose into the sky above the facility, an AFP photographer reported.
"The fire started in one refinery before spreading to another," the civil defence agency said in a statement.
"More than 10 people were injured, mainly men from the Arbil civil defence," it said, adding four fuel tanks and three fire trucks were burned.
The fire still raged at midday on Thursday despite the deployment of 30 rescue teams who were trying to prevent it from spreading further, the agency said in a later update.
With Iraq experiencing scorching summers, the country has seen multiple fires in recent weeks, affecting shopping centres, warehouses and hospitals.
Iraq is one of the world's biggest oil producers and crude oil sales make up 90 percent of Iraqi budget revenues.
But exports from the Kurdistan region have been halted for more than a year in a dispute over legal and technical issues.
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