The fire was small and extinguished quickly, the report said, but left people with severe smoke inhalation due.
The fire broke out during maintenance work, a spokesman for the Jubail and Yanbu industrial zone, Abdel Rahman al-Abdel Khader, told the agency.
The victims suffocated from fumes of burning chemicals, he said. Another 11 employees were injured, six of them left in "serious state".
United is a subsidiary of Saudi Arabia Basic Industries Corp 2010.SE (SABIC).
Spokesmen for SABIC and United could not immediately be reached for comment.