The incident caused schools to be placed into lockdown and police urged all members of the public to avoid the area.
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Superintendent Naila Hassan, Waitematā District Commander, says the incident occurred when a police unit "performed a routine traffic stop" on Reynella Dr.
"There has been shots fired at police officers," he said. "Two officers have been shot and have been seriously injured. A member of the public has also been hit by the vehicle and has been injured."
Police had earlier sent "a large presence" to search for the alleged offender.
Witnesses told Newshub they heard several gunshots at about 10:45am on Friday. The Armed Offenders Squad (AOS), an Eagle helicopter and a Westpac helicopter were all called in.
One nearby resident said she heard "loud bangs, then the police helicopter circling our place". She said there were "heaps of police cars, ambulances, and two cars of AOS" and "police running around with guns".
"I was in my lounge and I heard what I now know to be gunshots, however, it did sound like a car backfiring, quite close to my house," another person told Newshub.
"I initially thought nothing of it until I started seeing the helicopter circling quite low and quite close to my house. A whole bunch of police cars just flew by my place, which is when I realised it was quite serious."
Massey High School said it had taken the precautionary measure of entering lockdown on the advice of police.
"We are unaware how long this will last," a statement on its website reads. "Please do not try to contact students at school. Everyone is safe in class."
One student told Newshub about 120 students had been locked down together in the school's gym.
"Many are just playing with PE equipment but the teachers are trying to get everyone to stay sitting down," one student told Newshub. "I don't think most know of the events that are happening."
Others said pupils and teachers were locked in classrooms with the blinds pulled down, or had covered their windows with towels and paper.
"There is no sign of any people entering or exiting school classes. Teachers are starting to find some stuff for us to go toilet," one said.
Witnesses told Newshub at least six ambulances were seen on Reynella Dr, while at least nine police cars were seen heading to the scene at speed.
Police told Newshub details were still being confirmed, and further information would be released when it became available.
"Police advise all members of the public to avoid the Massey area, in particular the areas around Don Buck Rd, Waimumu Rd, Hewlitt Rd and Triangle Rd."
Auckland Transport urged motorists to avoid the area, warning there were diversions in place affecting all traffic, including bus services.
A witness said the scene quietened down within an hour of the incident, but a heavy armed police presence remained on Hewlett Rd for much of the day.
A resident said there were six officers with firearms stationed outside her house, "looking like they are waiting for something to happen".
She says the incident hasn't changed her view of the neighbourhood, which she says is "generally pretty quiet" and "such a beautiful place to live".
"All areas of Auckland have things go down. I don't find it concerning. I am not scared of where I live now."
She has two children under five, and says she's had to think hard about how much to tell them about what's going on outside.
"I have just told them we have got some police looking after us outside because somebody has done something that they shouldn't have done. Just got to keep it age-appropriate."