Rhona Martin became a household name when she led the Scots-born squad to glory at the 2002 winter games when she released her 'stone of destiny' in the final.
But thieves stole her medal, along with a 1924 Olympic medal and other curling memorabilia worth more than £34,000 in a raid on Dumfries Museum.
Ms Martin said: "I am absolutely devastated and gutted to have been informed by police of the theft of my Olympic gold medal. I would directly appeal to those who have taken this to return it."
It was part of an exhibit set up following Scot David Murdoch's Team GB in winning silver at the Sochi games in February this year. Among the items also stolen were a gold medal awarded to British skip Willie Jackson at the first Winter Games in 1924, four other historic curling club medals, a silver gilt cask and the Provost's chain of the Burgh of Maxwelltown at Dumfries.
Thieves smashed their way into the museum at about 10pm before breaking open display cases and helping themselves to the contents and fleeing the scene.
Millions stayed up late to watch Martin lead her team to victory and she was awarded an MBE for services to the sport.
She has toured schools throughout Scotland with her medal to inspire children to take up sport.
Martin said: "I have had the pleasure of sharing the medal with so many people since I won it with the stone of destiny in Salt Lake City in 2002. It obviously had a lot of sentimental value. With all the hard work and dedication it took to get to the Olympics, that was my reward. The medal is not only mine, it is all of Scotland's and was on display in the Dumfries museum so that everyone can share it. After such a fantastic year for the sport and with the Commonwealth Games rapidly approaching, this is an ice cold bitter blow for me, my country and the traditional 500-year-old Scottish sport I have loved my whole life.
"I can't get my head around it - it's no use to anybody else and they can't show it off. I would urge whoever has it to return it."
Murdoch, who lives in Lockerbie, said stealing the two gold medals amounted to a "theft of Scottish sporting history" and had put a "black cloud" over curling.
Police estimate the value of the items was in excess of £34,000.
Bruce Crawford, chief executive officer for the Royal Caledonian Curling Club which had loaned to medals to the museum, said it was impossible to attach a monetary value to them. Mr Crawford, also a trustee of the Scottish Curling Trust, said: "That gold medal has inspired so many people and has brought people to sport. They have learned that it is possible for a girl from Scotland to win a gold medal at the Olympics.
"It beggars belief that someone can do this. They had been lent so that they could be shared with other people. Rhona will not be interested in insurance money or having a replica made, she'll have her heart set on finding where it has gone and retrieving it. The whole sport and sporting community will be worse for the loss of these items."
Police want to trace three men wearing dark clothing seen in the area around the time.
Chief Inspector Steven Lowther said: "We are keen to trace the three individuals seen running away from the Museum around this time. It goes without saying that these items are distinctive and hold a huge amount of emotional attachment to the owners. We hope that someone may have some information on the location of these items, if they do, we would urge them to contact us."