The fire started outside the Pennine View facility at 6pm on 8 June, with fire services from West Morley attending the incident. The fire was fully extinguished by midnight.
It is understood that workers at the site used forklift trucks to break up burning material during the operation.
DS Smith confirmed that a full internal enquiry is currently underway and said that no further details were available until the results of that process are known.
A spokesman said: "Health and safety is a vital part of DS Smith's approach to business and the company is committed to ensuring that health and safety takes priority at all times."
The fire service was unavailable for comment at this time.