The dress was worn by Moss in September when she arrived with fashion photographer Mario Testino at a party at the Victoria & Albert Museum in celebration of its new exhibition on Dior.
A tear at the shoulder appeared when someone trod on the vintage cream satin and a gaping hole emerged later across the back.
By the time Moss moved to the Dorchester to carry on partying, she had been forced to hitch the dress up and tie it around her waist. She was last seen in the battered number at about 3am.
It is one of around 30 items given to help the charity's fund-raising drive.
James Brown, a former Elle Style Awards hairdresser of the year, said: "I know first-hand the devastating effect cancer can have so I jumped at the chance to do something to help.
Half the items can be viewed online for bidding at the James Brown Collection eBay shop a week from today. The highest bids at close of play next Friday win.
The other half will be available for viewing at the Cancer Research UK shop in Marylebone High Street next Friday.
