Police and ambulance were called to the area, near Henderson Rd and Whitby Cres, about 2.10pm today.
One person has been taken to Hawke's Bay Hospital with serious injuries, a St John spokeswoman said.
The shooting took place on the grounds of Flaxmere Primary School, which was placed in lockdown about 2.15pm.
Police said they were not seeking anyone else in relation to the shooting.
"Police were initially advised the man was carrying a firearm, and attending officers were armed," they said in a statement tonight.
"The man was located by police with what appeared to be a firearm and he was shot once.
"The officers immediately administered medical attention and the man was taken by ambulance to hospital where he's reported to be in a serious but stable condition."
They said the students "were kept safe" throughout the incident.
"Police deal with dynamic and fast moving critical situations every day and our absolute priority is safety, in this instance the students and staff members.
"The officers involved are being offered every support."
The Independent Police Conduct Authority would be notified.
Peterhead School nearby was also placed into lockdown for five minutes. The lockdown at Flaxmere Primary was lifted just before 3.30pm.
Scary but kids were amazing, says teacher
Flaxmere Primary School teacher Phillippa Watson said it was "scary for the kids, but the kids were amazing".
The school intercom helped police communicate to everyone what to do during the lockdown, she said.
"It was really frightening for everyone."
One pupil in one of the classrooms of the school described a frantic rush to shut the curtains, close the windows and lock the doors.
It was their last day of school for the year, the pupil said.
"We were just hiding and tucking ourselves in.
"We all thought it was fake because we do practices but then we heard the intercom say, 'it's not a drill' and we were like 'oh hell really'.
"Some people were really scared so others were saying "it's okay". Our teacher was saying "it's okay, just be quiet then you'll be safe"."
"We heard the intercom again and our principal said "it's okay the police are here. I'm going to go over [to them] and go to all the classes to take them [the kids] out front.
"'If I don't come inside your classroom stay quiet and be safe'. So we just stayed in there and waited until she came and got us."
A parent who was outside the school at the time of the incident told Hawke's Bay Today she heard a gunshot ringing out.
"I was here to collect my babies. That could've been my babies," she said.
She was among roughly 100 parents waiting for almost an hour for the all clear to pick up their children outside the school.
Parents largely communicated with teachers via text who informed them that their children were safe in their classrooms throughout the ordeal.
