McGuinty said the fire was still burning Saturday evening.
"I cannot recall an incident like this in recent memory," he added.
The municipality of Wainwright said the fire had spread beyond the military base's perimeter into the surrounding area.
However, local officials said no evacuation orders had been issued.
Canadian Prime Minister Mark Carney addressed the incident in a post on X.
"A serious incident creating a major fire has occurred at CFB Wainwright, in Alberta," Carney wrote. "Our thoughts are with all the brave women and men affected."
Alberta Premier Danielle Smith described the incident in a post on X as a "significant and tragic fire" that affected military personnel at the base.
The Canadian Armed Forces, Royal Canadian Mounted Police (RCMP) and local emergency personnel were responding to the incident, according to the Canadian Broadcasting Corporation (CBC).
"The Canadian Armed Forces, the Department of National Defence, partners across the federal government, including public safety, are working with the government of Alberta and municipal governments to mobilize all necessary support," McGuinty said.
Canadian Forces Base Wainwright is located roughly 130 miles east of Edmonton and had approximately 1,310 military and civilian personnel stationed there in 2021, according to census figures cited by Reuters.
The nearby town of Wainwright has a population of approximately 6,600.
It was not immediately clear what caused the incident.
Reuters contributed to this report.