Four soldiers died in a fire at a training area at the Wainwright military base at 4 p.m. on Saturday, local time.
Many of the injured have suffered severe burns and face weeks, potentially months, in hospital, according to Danielle Smith.
Firefighting efforts were hampered by strong winds, and the flames quickly spread to the surrounding area. On Sunday morning, the fire was reported to be under control.
Wainwright military base is one of Canada's most active military training bases, where soldiers train and prepare for combat operations. The base has just over 1,000 personnel.