Power lines and branches were knocked down by wet, heavy snow that fell across the region on October 28.
Danielle Gauvin of Hydro One says most of the affected customers are in the Arnprior, Brockville, Winchester, Perth and Vankleek Hill areas.
She says about 60 crews are carrying out the repairs, which the utility hopes will be completed by the evening of Oct. 29.
Hydro One is also trying to restore power to about 2,700 customers in the London and St. Thomas areas of southwestern Ontario.
The first storm heading into the season delivered several centimetres of heavy, wet snow and ice that downed power lines, trees and branches.
Overnight snow also caused traffic delays in Toronto this morning as OPP officers responded to early-morning rollovers in the southbound lanes of Hwy. 400 between Hwy. 7 and Finch Ave. W.