The blaze "erupted during maintenance work" on the unit at Mina al-Ahmadi refinery, 40 kilometres (25 miles) south of Kuwait City, state-owned Kuwait National Petroleum Company (KNPC) announced on Twitter, according to France 24.
It said 10 people were injured, five of them hospitalised with severe burns. Firefighters were mobilised and had extinguished the blaze.
KNPC said Kuwait's refining operations and exports were unaffected, as the unit affected had already been out of service.
KI/PR