The colourful tapestry, which celebrates life, people and events across the centuries, on 77 panels, will have to be moved to a temporary base.
It was made by 4,000 people from 15 different countries.
Staff, who rely entirely on ticket prices and items sold in the shop, are now trying to fundraise to meet the cost of the repair work.
"If we can find an empty town centre shop we can turn this disaster into something good by taking the panels to the people.
"A temporary central venue within the town will be handier for people to see the panels and we can also promote our real home.
"We will waive the usual entrance fee so people can come and enjoy the Tapestry for free."
The centre's cafe is unaffected by the work and will remain open.
Some of the panels will still be displayed at the full time home of the Tapestry at the Friends Meeting House on Stramongate.
More top news
A look ahead at the forecast for the Border region
A selection of some of the best sunrise pictures from across the region, sent in by ITV Border viewers.
Chilly start. Some frost in places, icy patches possible too. Cloud and sunny spells today, hazier in the west later