The storm that has already walloped the Virgin Islands, Bahamas and North Carolina has brought hurricane-force winds to far-eastern Canada, knocking out power to hundreds of thousands of people.
Dorian hit near the city of Halifax, ripping roofs off apartment buildings, toppling a huge construction crane and uprooting trees.
There were no reported deaths in Canada, though the storm was blamed for at least 49 elsewhere along its path.
The US National Hurricane Centre said the post-tropical cyclone was centred about 55 miles east-northeast of thinly populated Anticosti Island on Sunday morning and had top sustained winds of 80mph.
It was heading to the north-northwest, roughly up the St Lawrence River.
Nova Scotia officials asked people in the province to stay off the roads so crews could safely remove trees and debris and restore power.
The government said that up to 700 Canadian military personnel will be fanning out across the Maritimes to help restore electricity, clear roads and evacuate residents in flooded areas.
Nova Scotia Power reported 380,000 customers were in the dark.
As the storm ploughed into Prince Edward Island, about 50,000 homes and businesses were soon without power, as were another 74,000 in New Brunswick.
By far the greatest devastation caused by the storm was in the Bahamas, where Dorian struck a week ago as a Category 5 hurricane with 185mph winds, and then hovered just offshore for more than a day and a half, obliterating thousands of homes.
Planes, cruise ships and yachts were evacuating people from the Abaco Islands and officials were trying to reach areas still isolated by flooding and debris.
The country’s National Emergency Management Agency said it was sending in extra staff because operations had been hampered by the storm’s impact on local workers.
The agency said it was setting up shelters or temporary housing for the newly homeless across the islands and appealed for Bahamians to take in storm victims.
The government said at least 43 people died due to the storm.
Dorian was blamed for five deaths in the US south east and one in Puerto Rico.