A St John spokesperson said they responded to reports of an assault in Onehunga at 2.30pm.
Police confirmed that a person had died following the incident.
They said they were trying to locate the offender who had been identified through CCTV footage.
A senior detective at the scene told RNZ a weapon was involved.
Earlier, the person was taken to Auckland City Hospital in a critical condition.
A police spokesperson said they were investigating.
In a statement, police said parts of Captain Springs and Church Rds remain closed while emergency services respond.
"Motorists are asked to avoid the area and expect delays while the incident is resolved."
Auckland Transport confirmed the assault took place on board the number 74 bus service in Onehunga.
AT director of public transport Stacey van der Putten said: "We are working with our bus operator to provide support to the bus driver who witnessed this incident as well as our other customers who were onboard at the time.
"The safety and wellbeing of our passengers and bus drivers is our top priority and we are engaging with police and our bus operator to fully understand this afternoon's incident."
