Pte. Steven Allen, 20, of Victoria, was standing in a lookout tower at CFB Wainwright around noon Monday when the structure collapsed.
The military said he was airlifted to an Edmonton hospital where he succumbed to his injuries Thursday.
Another soldier who was standing in the lookout tower with him was not seriously hurt.
Allen joined the military last fall and completed his basic training course earlier this year.
He was training at Wainwright to become a fully qualified infantry soldier in the regular forces.
Fraser Logan, a military spokesman, said the circumstances of the collapse of the lookout tower are under investigation.
The wooden tower was on top of a metal storage container.
"I can't speak for this particular incident but in the past anything of this nature, especially with the loss of life of a Canadian Armed Forces member in a training situation, a board of inquiry would be convened," he said.
This is second training death at the sprawling base this year.
Lt.-Col. Dan Bobbitt died when the light armoured vehicle he was in rolled during training manoeuvres in May. Four other soldiers were hurt in the same accident.
Bobbitt was commanding officer of the 2nd Regiment, Royal Canadian Horse Artillery based in Petawawa, Ont. The injured soldiers were members of the same regiment.
Prime Minister Stephen Harper expressed his condolences Thursday to Allen's family.
"This tragic incident reminds us of the trials that our brave men and women in uniform go through as they train to defend our freedoms and liberties," Harper said in a statement.
"Private Allen lost his life in the line of duty. We will honour and remember his service to Canada."
Defence Minister Rob Nicholson and Brig.-Gen. Wayne Eyre, commander of 3rd Canadian Division and Joint Task Force West, also expressed their condolences.
“The loss of any soldier is devastating to the military community," Nicholson said. "An investigation will be conducted into the circumstances surrounding this incident to ensure that every precaution is taken to protect the safety and security of our soldiers.”
Lt.-Gen. Marquis Hainse, Commander of the Canadian Army, said the "tragic accident serves to remind us of the dangers that the men and women who serve in the Canadian Armed Forces face each day, whether they participate in training exercises at home, or while deployed on operations abroad.
"We train as we fight in war. A loss of life in training is no less significant than a loss of life in war."
CFB Wainwright, about 200 kilometres east of Edmonton, is one of the busiest army bases in Canada.
It was used extensively to train thousands of troops before they deployed for service in Afghanistan.
Other soldiers have died at the base while training in 2008, 2007 and 2005.
— By John Cotter in Edmonton