Buchanan Galleries was open again for business at the weekend, but an investigation is continuing into the cause of the blaze, which broke out in a cavity wall on the ground floor on Friday morning.
It forced the centre to close at 10.40am for the rest of the day, costing traders hundreds of thousands of pounds.
A spokesman for the centre said bosses did not know the extent of the damage caused by the fire.
He said: "We do not know how much damage has been caused by the fire. That's a question for the Scottish Fire and Rescue Service."
A spokesman for the Fire and Rescue Service said it was not yet possible to summarise the extent of the damage but more information would be available later today.
No one was injured in the blaze, which was discovered when white smoke began pouring into the Galleries.
The centre was evacuated and stayed locked down all Friday while firefighters tried to bring the situation under control.
They had to demolish walls to access the cavities and extinguish the fire.
Pedestrian areas surrounding the Galleries in Buchanan Street, Sauchiehall Street and Killermont Street had to be cordoned off.
Dozens of fire engines and support vehicles were in attendance, while police helped with traffic and crowd control.
As well as the centre, several commercial properties in Sauchiehall Street were closed as the operation went on.
But it was business as usual on Saturday and Sunday as bosses decided to reopen the centre.