The CH-147 medium-lift Chinook helicopter landed west of the city in the dangerous Panjwaii district, Postmedia News reported.
Eight people suffered minor injuries, the International Security Assistance Force said.
The reason for the rough landing and the fire was not known. An investigation is under way, said Maj. Daryl Morrell, a Canadian military spokesman.
The ISAF and Afghan security forces secured the area around the helicopter, the Postmedia News said.
A Taliban spokesman has claimed responsibility for bringing down the aircraft and that people have died, but the Postmedia News said the Taliban often make false reports.
Canada's helicopters in Kandahar bring troops and supplies to dangerous provincial regions and, like other low-flying aircraft, are sometimes subject to enemy fire, the Postmedia News reported.