Retailers and other traders at the centre were given a week's notice to vacate the site after a mall boss revealed it was going into liquidation.
The tenants received a letter from InShops' chief executive Frederic Bonnet, saying the centre was preparing to appoint liquidators.
Shop owners spoke of their shock at the move -and now fear for the future.
There are around 60 to 70 traders in the Savoy, which is one of the city's top indoor markets and is visited by around 47,000 people a week.
Businesses include cafes, furniture shops, food outlets and clothes shops.
In the letter, dated January 10, Mr Bonnet said: "Traders and sub-tenants need to vacate the sites prior to the close of business on 17 January 2014".
He wrote that InShops Centre Limited and InShops Starters Limited had, "suffered from increasing losses and are now unable to generate sufficient cash to allow them to continue."
He added that the firm had been working with advisors to try and find a solution but despite this, the directors, "have concluded that the business can no longer continue to trade," and, "it is necessary to appoint liquidators to wind up the companies."
Other shopping developments run by the company across the country have also been hit.
Father-of-three George Rogers, 37, from Clydebank, runs a shoe repair and key cutting business in the Savoy Centre with his brother Stewart.
They have been at the site for 12 years and opened another branch further up on Sauchiehall Street six months ago.
Mr Rogers, who is a former manager of the centre and used to be head of the traders' committee, said: "We couldn't believe it when we turned up at work on Friday and got these letters.
"A lot of the traders are really worried - this is their livelihood.
"We have been in the Savoy for 12 years and don't want to leave.
"We feel like we're in limbo - we don't know if it's over for us.
"We can only hope that someone will come in and start opening a dialogue with us."
The tenants hope they will be given a lifeline, after the letter said the landlord had, "expressed an interest," in running the operation after the firm went into liquidation.
Belfast-based property group PBN is the owner of the Sauchiehall Street site.
However, negotiations are ongoing and it is unclear exactly what is going to happen.
Mr Roger added: "It's shocking that InShops have left us in such a position.
"Where and how do we figure in future plans or developments?"
Mr Roger's brother Stewart, 35, said he was hopeful there would be a positive outcome.
Concerns have been raised in the past that the Savoy has failed to move with the times and has been left to rot.
Stewart Roger added: "The Savoy has a lot of potential and most traders want a bit of work put into the centre.
"That could come if it is taken over but we're worried about the terms changing."
Accountacy giant KPMG has organised a meeting of creditors to take place on January 21 in Manchester.
KPMG official said creditors will be asked to consider a resolution to appoint liquidator or joint liquidators at the meeting.
Despite attempts to contact InShops, there has been no response.
InShops Centres Ltd is a Geraud UK Ltd subsidiary. Its headquarters are in Liverpool, where the company's management and administration teams are based.