The refinery is one of many energy infrastructure facilities hit by fire or drone attacks across Russia in the past week.
"The vacuum unit was on fire. According to preliminary information, there were neither casualties nor injured," Sergei Boiko, the head of Tuapse district, said on the Telegram messaging app.
The plant's annual capacity is 12 million metric tons (240,000 barrels per day). It supplies fuel mainly to Turkey, China, Malaysia and Singapore. The plant produces naphtha, fuel oil, vacuum gasoil and high-sulphur diesel.
The cause of the blaze and the scale of the damage were not immediately clear. A Rosneft representative was not immediately available for comment.
Unofficial Telegram channels showed pictures of the blaze and said drones had been responsible.
Russian energy company Novatek (NVTK.MM), opens new tab on Sunday said it had been forced to suspend some operations at the huge Baltic Sea fuel export terminal and "technological processes" at its fuel-producing complex after a fire started by what Ukrainian media said was a drone attack.
Russian news agencies also quoted officials at the region's major airport in the seaside town of Sochi as saying it had suspended arrivals and departures. Crews and dispatchers were taking all precautions to ensure flight safety in the area.
