It is not believed a weapon was involved in the fight.
Counties Manukau police also responded to the scene on Nesdale Avenue.
"The matter is currently under investigation by Counties Manukau CIB. Police are speaking to a number of people at the scene who are assisting with inquiries," police issued in a statement this afternoon.
Police were not looking for anyone else in relation to the incident.
A post mortem is scheduled for tomorrow which will give an indication as to the cause of death.
"The investigation is in its early stages," Detective Senior Sergeant Albie Alexander said.
"Preliminary witness accounts indicate that an altercation had taken place, however until all witnesses have been identified and spoken to, police are unable to make further comment on the circumstances of the death."
Foodstuffs North Island managing director Murray Jordan this evening confirmed the incident took place at their South Auckland warehouse.
"We can also confirm, with a sense of shock and deep regret, that an individual died despite the best efforts of ambulance staff. Police are currently on site and have taken charge of the scene."
The supermarket giant was providing support to the family of the dead worker, they said.
"They are the first focus of our efforts and we will be providing every possible level of support we can. We are also providing counselling and support for our staff and will continue to do so for the foreseeable future. This will remain our focus over the coming days as the police progress their investigation."