The fire department said the blaze was apparently caused by chemicals exploding at the plant in Mina Abdullah near Kuwait's second largest oil refinery, according to state-run Kuwait TV.
A security source said one Indian worker suffered minor burn injuries in the blaze, but he did not mention an explosion, adding that firemen promptly put out the flames.
The plant is run by the privately-owned United Petroleum Projects Company, a Kuwaiti company that deals with oil products.
National refiner Kuwait National Petroleum Co said in a statement that no explosion or fire occurred in the Mina Abdullah refinery itself.
Kuwait is Opec's fourth largest oil producer, pumping around 2.5 million barrels per day.