Fredericton, the capital of in New Brunswick province, has a population of about 60,000.
One person was in custody, they said, and there was no further threat to the public.
A spokeswoman for Dr. Everett Chalmers Regional Hospital said it is treating multiple victims in the Fredericton shooting.
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.
Burns had served with the Fredericton police force for two years, as well as an auxiliary officer for two years prior. @CityFredPolice will continue to release information.
He said that about five minutes later he could hear similar sounds near his home.
Genine Patricia Paul-Dimitracopoulos met Constable Costello almost 15 years ago in her role as a social worker with St. Mary's Child and Family Services.
Friday's shooting occurred three weeks after a gunman walked down a busy Toronto street, killing two people and wounding 13 before killing himself.
"With RCMP support, this developing situation is under investigation by Fredericton Police".
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"But broadly speaking, the government of Canada is obviously taking the issue of gun violence very seriously".
Firearms laws in Canada are stricter than in the U.S. but a proliferation of weapons has led to an increase in gun-related crimes in recent years.
There were between six and 11 homicides a year in New Brunswick between 2012 and 2016, according to Statistics Canada.
Canadian prime minister Justin Trudeau said: "Awful news coming out of Fredericton". "During this hard time, our thoughts are also with the courageous women and men on the front lines working to keep us safe", said Gallant.
In 2014 in another mass shooting in Moncton, New Brunswick, three Royal Canadian Mounted Police officers were killed and two more were wounded.
The three others killed in the violence were Const. Robb Costello, a father of four, Const. Sara Burns, who was married with three children, and a woman whose identity has not yet been publicly confirmed.
Costello, 45, was a 20-year police veteran, while Burns, 43, had been an officer for two years, and an auxiliary officer prior to that. "I'm on my floor", he said.
"It's not something that we expect in Fredericton to wake up and hear about".
Gallant said he was working in his Shediac Bay-Dieppe riding office Friday morning when his chief of staff called to let him know what happened, and made his way to Fredericton after that.
Jackie McLean says a police inspector told her family that her common-law partner Robb Costello was among the four people who died in a shooting at an apartment complex.