The gallery and full exhibition programme will remain open to the public during the renovations.
The unique architecture of the building such as distinctive roof lines will be retained with special detailing.
Aside from minor alterations, the current roof is largely the originally built roof from the 1970s.
The building was designed by local architects Natusch, Wilcox & Co and was expanded to its current size in 1975.
The spokesman said disruptions would "be kept to a minimum, although there may be some noise and some programmes may need to be moved around the building as required".
Three exhibitions are being held over summer: Leanne Morrison: Off the Edge, Richard Brimer: Harvest and Andy Leleisi'uao: Kamoan Mine.