Baghdad firemen were struggling to put out the blaze and called for help at the refinery in the southwestern Baghdad suburb, the official said.
With local firemen unable to put out the blaze, fire departments from outside Baghdad had to be brought in to help.
The Dura refinery also houses Baghdad's main power plant. The refinery provides fuel for the plant, which powers most of Baghdad and outlying areas.
It was not immediately clear if the fire had affected the power plant, AFP said.