The port was closed for an investigation after the incident and police said WorkSafe was investigating.
Ports of Auckland CEO Tony Gibson said: "We are devastated by this news. This is a terrible time for his family and friends, and we will continue to stand alongside them and support them.
Everyone who works at Ports of Auckland has been deeply affected by this accident. We have been providing staff with support and we will continue to do everything we can to help people through this difficult time."
More than 20 workers have died on the job this year, mostly in forestry and farming industries.