The 33-year-old from Prestwich, who has asked not to be named, suffered burns to his wrist, leg and groin and singed his facial hair while removing a lamp post on Harper Fold Road in Radcliffe on 9 June 2011.
The council was prosecuted by the Health & Safety Executive (HSE) after an investigation found he had received inadequate training and supervision for the work.
Trafford Magistrates' Court heard how new street lights had recently been installed on the road and the old lights had been disconnected.
The injured worker and a colleague were in the process of removing one of the old lamp posts, using a jackhammer to break the concrete around the base, when he struck a mains electricity cable.
The HSE discovered that the two workers had not been given service drawings for the lamp post they were removing, which would have shown where the mains cable ran.
Bury Metropolitan Borough Council, of Knowsley Street in Bury, was fined £20,000 and ordered to pay £7,594 in costs after pleading guilty to breaching the Health and Safety at Work etc Act 1974 by failing to ensure the safety of workers.
Speaking after the hearing, HSE principal inspector John McGrellis said that the council worker could easily have been killed. "He shouldn't have been put in a situation where he didn't know what the potential dangers were as he used a jackhammer to break up the concrete around the lamp post. It's vital that people carrying out work near to power lines receive appropriate supervision and training to ensure their safety."