Four service members are confirmed to have died, Carney said on Sunday.
He also said "dozens" had been "seriously wounded", without providing further information on their conditions.
Prior to Carney addressing the nation, Canadian media reported the death toll as seven citing unnamed military sources.
The prime minister did not indicate whether or not the government expects the death toll to rise.
The names of those who lost their lives have not been identified but their families have been informed.
On Saturday evening, Royal Alexandra Hospital in Edmonton declared a code orange - a disaster response protocol for a high-casualty incident. It was stood down on Sunday afternoon.
Alberta's health service said the emergency response lasted for 10 hours, and involved 22 ambulances and eight aircraft.
Ongoing care for the injured is expected to be "intensive", a statement continued.
A stream of ambulances were seen arriving at the hospital and one doctor told Canadian public broadcaster CBC that the facility had been "completely overwhelmed" by the number of patients.
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