The powerful storm hit Halifax on Saturday with winds of 100mph (160km/h), toppling trees and cutting power to more than 450,000 homes.
Canada's Public Safety Minister Ralph Goodale said the military would be deployed to help recovery efforts.
It comes days after Dorian devastated the Bahamas. The death toll there is 43 but is expected to increase further.
The hurricane has since moved up the US eastern seaboard. The Canadian Hurricane Centre labelled it a "very intense post-tropical cyclone".