A young man was arrested after a manhunt was launched following the incident in the state capital, Raleigh, on Thursday.
At least two other people, including a second police officer, were wounded and taken to hospital, Mayor Mary-Ann Baldwin told a news conference.
“We must do more. We must stop this mindless violence in America. We must address gun violence,” Ms Baldwin said.
The shooting occurred shortly after 5pm local time near the Neuse River Greenway trail, which runs through part of the city, Reuters reported.
The manhunt turned districts into crime scenes flooded with first responders as residents were told to take shelter.
About three hours later, police had the alleged gunman “contained in a residence”, Ms Baldwin said. He was arrested shortly afterwards.
The alleged shooter is thought to be a white male teenager who had a rifle, WTVD television reported.
Helicopter video footage from WRAL television showed more than 10 emergency vehicles lined up on a road in a wooded area, one of several crime scenes.
State and local law-enforcement agencies are involved in the “active investigation”, Ms Baldwin said.
Raleigh Police Lt Jason Borneo said the motive for the shooting would become clearer in the coming days.
North Carolina Governor Roy Cooper said: “Tonight, terror has reached our doorstep.”
“The nightmare of every community has come to Raleigh. This is a senseless, horrific and infuriating act of violence that has been committed.”
More than 34,000 people have died in shootings in the US in 2022 — with suicides accounting for more than half the number — according to the Gun Violence Archive website.
The North Carolina shooting occurred after a jury earlier in the day rejected the death penalty and backed life imprisonment for Nikolas Cruz, who shot and killed 17 people at a Florida high school in 2018.