A huge pane of glass from the gallery ceiling collapsed last week.
Visitors narrowly escaped injury when the 1.8m by 1.2m window shattered and fell 20 metres, showering a public walkway three storeys below with glass.
The unstable glass comes as a disaster for the gallery, which opened last month after a four-year $168 million facelift.
Gallery chiefs, engineers, architects and the State Government's major projects staff held crisis talks late yesterday.
NGV chief operating officer Liz O'Keeffe revealed engineers had warned more windows could break.
The suspect panes are in vertical glass windows that enclose two internal courtyards in the revamped St Kilda Rd complex.
"The advice we have received suggests there is a possibility of further breakages, and that we take temporary protection measures to ensure the safety of the public," Ms O'Keeffe said.
"Let me say, though, this glass has been installed for the past year, and what happened on December 30 was the first time there was any indication that breakage was possible."
Seven galleries were closed immediately after the incident at 12.30pm last Tuesday.
The glass fell more than three storeys on to the walkways below. The alarm was raised by a gallery attendant.
Officials only revealed the problem to the public after inquiries by the Herald Sun on Monday.
Engineers have suggested last week's extreme heat was to blame for the glass shattering.
The report said it could have been caused by "extreme heat mixed with some chemical reactions within the glass", Ms O'Keefe said.
The galleries will reopen next week, when exposed walkways are covered.
Ms O'Keeffe said she was satisfied the temporary cover would protect the public should more glass break. It is not known how long it will take to fix the problem or how much it will cost.
"It will cost somebody some money," she said.
"We don't know who will pay yet, and we don't know how much - it's too early to make any comment about those these things."
Deputy director Frances Lindsay tried to put on a brave face yesterday. "As you can see today, the building is absolutely filled with visitors," she said.
"We believe they are absolutely safe, and more importantly, they're enjoying so much of the collection," she said.
But the fear of shattering glass is not the only setback for the gallery, which opened just five weeks ago. Crowds have also been kept off the sculpture garden - an area earmarked for family picnics - because the drought-affected grass has been resown.
The building's critically acclaimed make-over was carried out by Italian architect Mario Bellini in partnership with architects Metier 3 in Melbourne. Metier 3 has declined to comment on the glass debacle.
While no decision has been made to remove the glass, one option might be to strengthen the existing panes.
The Great Hall, the water wall and galleries containing the NGV's masterpieces remain open to the public.