The staggering rise in exports is revealed in figures provided by HM Revenue & Customs.
Exports of salmon to the Far East went up from 682 tonnes in 2010 to 8675 tonnes in just the first ten months of 2012.
It appears the biggest increase was between 2010 and 2011, but the figure is still rising, with the exports in the first ten months of 2012 being worth £37 million to the Scottish fish-farming industry, compared to £28m for the same period of 2011.
Scott Landsburgh, chief executive of the Scottish Salmon Producers' Organisation, believes there are still substantial opportunities in the Far East for the salmon industry.
He said: "Sales have increased more than twelve-fold in three years and our market share still only represents less than 1% of the total current opportunity in the Far East."
Mr Landsburgh, whose organisation is the trade body for the majority of Scotland's salmon farming industry, added: "With rapid growth among middle classes looking for premium and healthy products, there remains plenty of scope for further market expansion in this rapidly growing market."
China is now the largest Far East market for Scottish salmon, 20 months after an agreement was signed to permit direct seafood exports to the People's Republic.
Richard Lochhead, Cabinet Secretary for Rural Affairs and Environment, welcomed the figures and pointed out salmon is increasingly being used for sushi and similar products in the Far East.
He said: "Our salmon is a healthy and highly sought-after product, renowned for its flavour and texture, and I'm sure that its popularity can continue to grow."
Last month saw the largest-ever Scottish food and drink trade mission to Japan and China, during which an agreement was signed by the World Association of Chefs Societies to promote Scottish salmon and langoustines to its 10 million member chefs in 93 countries.
Salmon is Scotland's largest food export, exported to 64 countries.
Anne MacColl, chief executive of Scottish Development International, said: "Scottish salmon is internationally regarded as being amongst the highest quality in the world, and is rapidly becoming the product of choice in the Far East.
"Our food and drink exports are at an all-time high and these latest figures show Scotland's world-class premium quality food and drinks are increasingly in demand across the globe."