It is the second fire to hit a major construction site in the city in three days.
Emergency services were alerted to the blaze at the Govan site shortly after 1pm and had the fire under control within 20 minutes.
The fire broke out in the second floor plant room of the £840m new hospital building, which is under construction and due to open in 2015.
A spokeswoman for the Scottish Fire and Rescue service confirmed no casualties were reported.
A joint investigation alongside Police Scotland will be launched into the circumstances surrounding the blaze.
Last Saturday more than 40 firefighters were called out to tackle a blaze in the domed roof of Glasgow’s other major building job for the new Scottish Hydro concert arena.
It has emerged the fire was caused by sparks from welding on the roof.
Contractor Lend Lease is presently assessing the fire and water damage to see whether it can still open the music arena in September as originally planned.
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