Those remaining without electricity are customers of the Vattenfall, Savon Voima and Suur-Savon Sähkö utilities. The companies said they hoped to restore power to nearly all customers by the end of the weekend, but that some areas would still take days of work to clear fallen trees and repair lines. In some areas, the entire electrical network must be virtually re-built.
As many as 40,000 customers suffered a blackout after the storm, which was dubbed Asta after Friday's nameday.
South Savo emergency officials using boats have begun rescuing people stranded by the storm on the Iiniemi peninsula near Sulkava. The road to the area, where there are dozens of summer cottages, remains blocked by many fallen trees. The cabins are without power while phone service is poor.
Power outages are also still affecting mobile phone service in various parts of Finland and there were persistent storm-related delays in rail service on Sunday in Eastern Finland.
The powerful storm sliced quickly across South Karelia to South Savo, with the worst damage around the city of Savonlinna. Asta packed winds gusting up to 20-30 metres a second. No injuries were reported.
The Federation of Finnish Financial Services estimates the storm damage at between 10 and 20 million euros.