Some 31 people, the dead man included, were found inside the container at Tilbury Docks, east of London.
The container arrived on a ship from the Belgian port of Zebrugge and was being unloaded by the Port of Tilbury authorities.
"Thirty-one people, including adults and children of both genders, were found inside," said an Essex Police spokesman.
"One man has sadly died and the others have significant health problems. They are being treated by ambulance crews and are being taken to local hospitals."
The East of England Ambulance service confirmed a hazardous area response team had been sent, including seven ambulances.
"Our initial priority is to assess the level and nature of any injuries, and ensure that those people in most need are treated first and taken to hospital," a statement said.