Police said they were searching for Justin Bourque, 24, who was “armed and dangerous”, and tweeted a picture of a suspect with weapons.
Officials have warned people to stay inside and lock their doors.
The Royal Canadian Mounted Police said the officers were shot responding to reports of an armed man wearing camouflage clothing.
That initial call was at 19:20 local time.
The two wounded Royal Canadian Mounted Police officers were taken to hospital with non-life threatening injuries, a police spokesman said.
Mayor George LeBlanc said: “This is a terrible loss and a tragedy for the families.”
Officers have blocked off a number of roads in Moncton and traffic is reported to be backed up on major routes across the city.
Drivers have been asked to stay away from the area.
In a statement, New Brunswick Premier David Alward said he was “shocked and saddened”.
“I would ask New Brunswickers, particularly in those areas identified by police, to follow the situation as it develops and to listen to the advice of police,” he said.
Witnesses said they heard the first shots in north-west Moncton at about 20:00 local time. More shots were reported about two hours later.
Correspondents say such violence is rare in Canada, particularly on the east coast.
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