Scottish and Southern Electricity Networks (SSEN) said that power has been restored to 98,000 customers in total since the start of the storm around lunchtime on Friday, however, 24,000 homes and businesses remained off supply on Monday.
SSEN warned that it does not expect power to be restored to some properties before Tuesday at the earliest, while "localised faults" may not be fixed until after that.
The company said it is working closely with local and national resilience partners to help coordinate the community response and support is being prioritised for the most vulnerable Priority Services Register customers.
Storm Arwen Scotland: Man dies as driver and police van crushed in Aberdeenshire by falling trees
Meanwhile, SP Energy Networks said that about 4,500 customers were still without power at 2pm on Monday.
More than 100,000 homes in Scotland lost power on Friday night due to the severe damage caused by the storm, which brought gusts of almost 100mph and claimed three lives in the UK.
Mark Rough, director of customer operations at SSEN, said: "The severity and prolonged nature of Storm Arwen has caused widespread and extensive damage to our network in the north east of Scotland, with significant and challenging conditions resulting in multiple instances of damage to several overhead line circuits.
"The extent of damage means the repair work needed is complex and often requires lengthy clearance of access just to reach the problem areas, with substantial tree cutting and re-erection of overhead network infrastructure.
"We continue to work closely with our local resilience partners to prioritise support for our most vulnerable customers."
Mr Rough encouraged any vulnerable customer who is concerned about remaining off supply, or anyone worried about a vulnerable relative or neighbour, to call SSEN teams on 105, and thanked customers for their patience.
In Aberdeenshire, all schools will be closed for pupils and staff on Monday and Tuesday as any storm damage is assessed.
SP Energy Networks said its teams continue to work around the clock to restore supplies for all customers left without power.
It said that as of 2pm on Monday in Scotland, 4,500 customers were affected, with the Borders, Dumfries and Galloway, Fife and the Lothians worst hit.