Around 300 homes and businesses in the city centre had the electricity supply disrupted following the incident.
It is thought the man, who has not been named, was severely burned in the accident, which happened yesterday lunchtime.
He was taken to Glasgow Royal Infirmary for treatment.
The incident happened at a building site at the City of Glasgow College, in the city centre.
Emergency services, including the NHS Emergency Medical Retrieval Service, raced to the scene at Allan Glen Place, at around noon.
It is not yet clear how the worker came into contact with the cable, which carries 45 times the household supply of 240 volts.
One worker, who did not wish to be named, told of hearing a loud bang.
He said: "I heard a huge bang, it sounded like an explosion. The fire brigade, ambulance and doctors, were here within minutes."
It is understood emergency services originally received a report of "an explosion" in the Montrose Street area.
The Scottish Fire and Rescue Service confirmed it received a call from ambulance control, following reports of a loud bang.
A spokesman for the service, said: "Crews reached the scene within minutes and immediately provided the casualty with emergency trauma care.
"The quick arrival of an expert team from the NHS Emergency Medical Retrieval Service allowed him to be passed to the care of doctors at the scene.
"He was transported to the Glasgow Royal Infirmary by ambulance."
In a statement, City of Glasgow College, said: "We can confirm that an employee of a sub-contractor of Sir Robert McAlpine, who was working on the site of the proposed new City Campus, has been admitted to hospital after suffering an electric shock following contact with a live cable.
"We hope that the employee makes a speedy recovery.
"Health and safety on site is of the utmost priority and Sir Robert McAlpine will conduct a full investigation as swiftly as possible.
"We await the outcome of their early report and details of any measures which require to be taken."
Following the incident, around 300 shops, businesses and homes were hit by a power cut.
Glasgow Caledonian University, the City Chambers, and Cineworld were among the buildings affected by the outage.
A spokeswoman for the university said: "We experienced an outage but the electricity was restored within the hour."
Scottish Power confirmed the power was restored by 12.40pm. A spokeswoman for Scottish Power, said: "Supplies to around 300 customers were interrupted for around 40 minutes.
"This was due to a third party working on a building site in the area damaging one of our cables. We apologise for any inconvenience this matter caused."
Meanwhile, the Health and Safety Executive (HSE) said it was aware and investigating the incident.
HSE inspectors are expected to visit the site to gather information.
Police Scotland also confirmed it attended the incident and was working with HSE staff.