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
Showers or longer spells of rain. Gales on Sunday
One of the world's most famous locomotives drew huge crowds in Cumbria today, as it arrived after a ten year, £4.2 million, restoration.
One hundred artworks have been donated to an auction, to raise money for victims of flooding in Cumbria.