Around 350 properties in the East End of the city were cut off after a BT power unit was damaged.
A mattress and piles of rubbish were set on fire in Tollcross Road and the heat melted the copper connections inside the cabinet.
The incident is believed to have taken place on Wednesday night. Engineers have been working since Thursday to repair the damage.
BT managed to restore temporary service to some customers on Thursday and worked through the weekend to restore service to other homes. However, some customers were still affected six days later.
A BT spokesman said it was hoped that the remaining customers would be re-connected yesterday.
It was initially thought that cable thieves had struck and a £1000 reward was offered by BT and Crimestoppers for information.
A BT spokesman said: "A mattress and rubbish was set alight beside one of our street cabinets on Wednesday night and the heat generated melted the copper connections inside the cabinet, cutting off service to around 350 premises.
"Engineers managed to restore temporary service to some customers on Thursday and worked through the weekend to restore service to the majority affected.
"Engineers are still at the site working to reconnect the last few customers and everyone should be back in service later today.
"While it was initially thought this may have been an attempt at cable theft, it is now being viewed as either malicious or accidental damage."
A spokesman for Scottish Fire and Rescue said: "Deliberate fire setting is an offence that causes a severe cost to communties and puts lives at risk. Our message to the public is, don't accept it, report it."
Last year a reward of £10,000 was offered to help convict thieves who steal metal from electricity substations.
The campaign, by ScottishPower Energy Networks, was launched in response to a surge in thefts and attempted thefts of metal, with 1435 such incidents recorded at the company's substations since January 2011.
According to the firm, this has resulted in 140,000 homes put at increased risk of damage, 50,000 homes in Glasgow losing power for 30 minutes in November 2011.