WorkSafe said: "We have been notified of an incident in East Tāmaki where a worker has become trapped in a piece of machinery. We are making initial inquires."
Visy Industrial Packaging business unit manager Peter Swanson said he could not comment yet on what happened.
"We are trying to work it out ourselves," he said.
"I have only just come back to the site from another site. I can't tell you any more."
The accident comes just two days after a man died in another industrial accident at Fletcher Easysteel in Onehunga on Wednesday.
Fletcher Building chief executive Ross Taylor said the Onehunga tragedy "has shocked and deeply saddened all of us".
"My thoughts and sympathies, and those of his teammates and managers, are with his family," he said.
WorkSafe is investigating that accident.