The 24 year-old man, whose name has not been released, died after a fire and explosion at the North Killingholme plant on Tuesday.
Unite’s national officer for construction, Tom Hardacre, said: “Our thoughts and deepest condolences go out to our member’s family at this tragic time.
“Unite puts the highest premium on health and safety in the workplace and we are calling for an immediate, independent and comprehensive inquiry into what happened at Lindsey.
“We would particularly like to know why further searches were not made when our member was unaccounted for in the roll-call when employees were evacuated.”
Refinery owner Total has shut the facility after the fire that also injured two people.
A spokesman said: “It is with deep regret that Total Lindsey Oil Refinery can confirm that there has been a fatality following the fire and explosion.
“All affected process units at the refinery are shut down and safely isolated. All other units remain operational.”
The refinery has recently been the focus of a series of protests by union members against the use of foreign labour in the engineering construction sector.