"This type of training is normal for soldiers in theatre and essential in helping them to maintain high levels of expertise," said Brigadier-General Daniel Menard, the commander in Kandahar.
An Edmonton native, Cpl. Baker, 24, served with the Loyal Edmonton Regiment.
Prime Minister Stephen Harper offered his condolences to Baker's family, saying he served valiantly in order to build a better future for Afghanistan.
"The courage demonstrated by Canadians on this mission speaks to their dedication to creating a better country for the Afghan people. Their commitment to this goal is not diminished by this incident," Harper added.
Governor General Michaelle Jean said Baker served bravely and generously to support Afghans’ hopes for security, justice and a better life. "He merits our wholehearted admiration."
Defence Minister, Peter MacKay, called Baker's death "a tragic loss for Canada and for the Canadian Forces."
Speaking personally about Cpl. Baker, Brigadier-General Menard, said Cpl. Baker had a laugh that lightened up any room. "Joshua had a laugh rumoured to cure cancer," he said. "No matter where you were or how down you got, his laugh would find your ears and bring a smile to your face."
The Brigadier-General described Baker as an "extremely passionate" person who loved his job. "Joshua was mentally tough, physically robust and had a personality that made him a natural leader," he said.
"He had a deep love for his family and worried constantly about them. He also had a deep love for his faith; it was something he took pride in and that gave him strength."
News of the soldier's death came as Canadian troops were taking part in Operation Moshtarak, the largest air assault of the Afghan war in neighbouring Helmand province.
American, British, Afghani and other coalition troops stormed the insurgent-held town of Marjah and the district of Nad Ali early Saturday morning.
Three Canadian Chinook helicopters helped ferry 1,100 coalition troops to Nad Ali, under the watch of four Canadian Griffon escorts.
The repatriation ceremony for Corporal Baker is tentatively set for Monday, February 15.