The geometric matt glass panels covering the exterior are one of the key architectural features of the Reid Building, which was designed by Steven Holl architects of New York and JM Architects of Glasgow.
However, a fault in several of the greenish-tinged panels, which provide the building with its "skin" of glass, led to them breaking after they were fixed in place.
Contractors who have been carrying out the work will now replace them before the new school building, which is home to design students, officially opens. The school said the problem would not add to the project's cost or affect the building's official opening date.
The glass panels were specifically created for the building, which is currently open to students but remains under construction until its official opening on April 9.
Some of the glass panels look to have been almost completely shattered, while others have more limited damage.
A spokeswoman for the Glasgow School of Art said: "There were structural problems with some of the panels and they will be taken off and replaced. It is a painstaking process and will take place as the streetscape is completed.
"The faults in the glass led to them breaking and we are getting new panels to replace them - it does not alter the cost or the opening date."
The Reid Building replaces the Foulis Building and Newbery Tower, which were demolished after being judged no longer "fit for purpose", and is phase one of the campus developments at Glasgow School of Art.
It houses offices and design studios, workshops, media labs, a lecture room, exhibition spaces and student areas.
It encompasses the student union building, which has been retained but upgraded, as well as a refectory, an "infinity" pool and a garden terrace.
The building is made of concrete and has five storeys above ground and two basement levels. Its key internal design feature are three large "driven voids of light", internal voids which run from the roof to the basement and are designed to filter natural light through the building.
It was named after Professor Seona Reid, former director of the art school, and stands on Renfrew Street in Garnethill.