Kjestrup described the man as a "valued employee" and would not say any more about him out of respect for his family.
Kjestrup said workers had been told to stay home after the incident, which happened about 7.30pm yesterday.
Emergency services were called to the site on Unity Drive, in Rosedale, after initial reports the victim had suffered serious injuries.
Police confirmed the death this morning, however.
Kjestrup said they did not know "a hell of a lot," but acknowledged that authorities - including WorkSafe NZ - are now investigating the circumstances of the man's death.
The death has now been referred to the Coroner.