In many places, the electricity grid has been destroyed and will need to be rebuilt from scratch.
Storm Alfrida hit hard across Uppland on Sweden's eastern coast, with winds of more than 30 metres per second uprooting trees and dislodging other objects such as signs and scaffolding, causing major transport disruption on Wednesday as well as widespread power outages.
The vast majority of the affected customers were located in Stockholm county.
In Norrtälje, one of the worst hit municipalities, fire stations remained open on Thursday so that local residents could collect water, charge their phones or have a cup of coffee.
Work has already begun on repairing power cables, with backup power plants flown by helicopter to islands in the archipelago. But Vattenfall and Eon, two of the power companies affected, said that large parts of the electricity grid need to be entirely rebuilt, and that the entire process could take more than a week.
"It's still quite difficult out there, and hard to keep up with it, so it will take time," Vattenfall press officer Lars-Åke Linander told the TT newswire.
"There are large variations locally on when it will be ready. We are prioritizing areas where there are a lot of people so that as many people as possible can get power back."
Meanwhile, power has returned to the eastern island of Gotland and phone lines were also working again after previous outages which even affected emergency lines.