The Glasgow School of Art has moved six inches since a massive blaze gutted it a week ago.
There are fears the structure could collapse “with no warning” because of the fire damage.
The blaze ripped through the building from around 11.20pm last Friday, spreading to nearby properties, including the O2 ABC.
Glasgow City Council leader Susan Aitken has asked people to stay away from the area, which remains sealed off.
She said: “Our building control officers are saying part of the building has moved quite significantly, about six inches.
“The elevation has shifted. There’s a danger that part of the building may collapse.
“If that were to happen, it could happen with no warning.
“Therefore it’s very, very important that no one enters the cordon – unless they are an accredited expert.”
It comes as police revealed they had received a report of a break-in at the nearby Campus on Sauchiehall Street around 3.20am on Thursday.
The bar is inside the cordon, which was put up to seal off the area after the fire at the Mackintosh Building, and police are investigating.
A spokesman said: “Inquiries are continuing following a break-in at premises on Sauchiehall Street, Glasgow at around 3.20am on Thursday June 21.”
The council said there had been other reports of people breaching the cordon, raising safety concerns, and urged people to stay away.
Glasgow City Council’s head of building control Raymond Barlow said: “I fully understand people’s desire to get back into their property and if we could safely do anything to facilitate that then we would.
“However surveys in recent days have shown us that the West and East elevations remain of significant concern.
“This means that there is a risk that parts of the building might fall into Scott Street or Dalhousie Street. This could happen without warning.”
More than 120 firefighters were involved in fighting the blaze.
There were no reports of any casualties, although some properties were evacuated.
The building, designed by artist and architect Charles Rennie Mackintosh and built between 1897 and 1909, was undergoing restoration after being damaged by a fire in May 2014. It was due to reopen in 2019.