Crew members from HMS Bangor, which is moored nearby on the River Clyde, attended before the fire service arrived at around 8pm last night.
A spokesman for the tower, at the Science Centre, said: "The Glasgow Tower has resumed operation today as normal, following an incident yesterday evening.
"Alerted by a member of the public, Glasgow Science Centre staff dealt with a minor incident, which was attended by Fire and Rescue Scotland. We are also grateful to the crew of HMS Bangor, which is currently berthed at Pacific Quay, for their support.
"This incident happened after the tower had closed for the day, and so the public faced no risk.
"Our engineers have been on site and carried out a thorough inspection and the problem was traced to a short-circuited cable. Engineers repaired the fault overnight and the tower is fully operational today."
The 417ft tower has been beset by technical problems since it opened in 2001, and was shut down in September 2010. It reopened on Saturday after a £1.8 million refurbishment, including new elevators and a revamped visitor experience.
The £9m tower holds the Guinness World Record for the tallest, fully rotating free-standing structure in the world.