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, and a police officer confirmed to Stuff the person suffered stab wounds to the upper body.
Earlier, the person was taken to Auckland City Hospital in a critical condition.
A police spokesperson said they were investigating.
A resident on nearby Victoria Street, who lives in a block of units, said police searched his home looking for the attacker.
The man said police told him they had been told someone had been seen running down the driveway.
"I didn't know what was going on at that stage, they just asked if I consented to my house being searched because their dog wouldn't leave the area so I let them in."
The man said there were between 15 to 20 officers, outside his home, who were mostly armed.
"It was scary - I don't know why they pin-pointed my house, but they didn't find anything here."
Police left his driveway shortly after 5pm, he said, but were still patrolling nearby hours later.
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."
