Cahonas Scotland put up the item for bid on Ebay on Thursday evening with a starting price of 99p.
But the price rocketed to £5,000 after just two hours - and the listing still has nine days to go.
The bidding frenzy started as soon as the scarf, worn by Heughan at this year’s New York Tartan Day Parade, went online.
After bids of £45, £50 and £200, an anonymous user dramatically raised the stakes by putting up £1,000 for the blue and green tartan scarf..
The same user made further bids before another person made a claim for the scarf with a £5,000 offer. He was matched in his efforts with his rival with a bid of £5,001 – which it currently sits at.
That price is expected to rise further, with the auction still having nine days to go until it reaches its climax on April 24.
The sale is part of an auction for the charity called ‘loosen up!’, which encourages celebrities from the world of TV, music, and sport to donate their signed ties and other clothing accessories – in order to raise funds for causes relating to testicular, breast and prostate cancer in men.
The sale also includes a ‘pocket jamie’, an 8” cut out of his character from Outlander, and a signed DVD.
Other items up for bid on the auction include a signed hat from pop sensation Bruno Mars, a signed scarf from Beatles star Paul McCartney and a signed tie from former Queen guitarist Brian May.
Andy Murray, Rafael Nadal, Sarah Jessica Parker, Rod Stewart, Lewis Hamilton and Bryan Cranston are some of the other stars who have donated to the cause.