A 48-year-old man from Fredericton was arrested at an apartment complex in connection with the shooting, which broke out in the area of Brookside Drive between Main Street and Ring Road around 7:10 a.m.
It is rare in Canada for police officers to be killed in the line of duty.
Two police officers were among four people killed Friday in a shooting that sparked panic and a police lockdown in a sleepy town in eastern Canada.
Several victims were being treated at a regional hospital, but there were no immediate details on the nature of their injuries or their conditions. They didn't identify him.
Sarah Williams, who lives close to where the shootings occurred, said she awoke to loud sounds.
Two civilians, a man and a woman, were also killed in the shooting.
"My handsome and talented Sara Mae is now the latest City of Fredericton Police Officer".
Const. Sara Burns grew up in Fredericton and joined the local police force in 2015, soon after graduating from the Atlantic Police Academy.
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Canadian public broadcaster CBC said that the shooting happened in a residential area of the city north of downtown, and that heavily armed police, paramedics and firefighters were on the scene.
"Awful news coming out of Fredericton", Canadian Prime Minister Justin Trudeau said on Twitter.
Police say they have one suspect in custody.
CBC reports that a local Tim Horton's coffee shop has been told to keep their doors locked and their customers and staff inside until further notice.
Jackie McLean, Costello's common-law partner, says a police inspector told the family the news Friday morning. "To see that there's actually fatalities is pretty extraordinary for this area".
Four people have died in a shooting in Canada.
Everett Chalmers Regional, "is now treating multiple victims of today's shooting", the local health authority said shortly before noon.