According to Devon and Somerset Fire and Rescue Service, the ambulance service called for assistance freeing a man from a machine on Saturday morning.
A spokeswoman for the service said that by the time the apparatus arrived the man had been freed.
John Stoddard, 41, was airlifted to the Royal Devon and Exeter Hospital where he later died.
A spokesman for DS Smith said: "It is with the deepest regret that I can confirm there has been a fatal accident involving one of our employees at Higher Kings Mill.
"We are doing everything we can to establish the full circumstances and have launched an investigation in conjunction with the relevant authorities. Our thoughts are with the employee's family and colleagues and we are offering them our support and assistance at this very difficult time."
The accident occurred just a few days after DS Smith announced that it would be selling the site to Asia File Corporation. However, the spokesman said that the incident would not affect the sale.