Smigun-Vaehi, who won two golds in Turin and a silver medal at the Vancouver Games in 2010 before retiring, said she had done nothing wrong.
"It is unbelievable, but I am now in a situation where I have to fight a new battle," she said in a statement.
"Exactly two months ago I received a message that no banned substances were found in the new testing of my A-sample given at the 2006 Turin Olympic Games, during the period 12 - 16th February, but that allegedly it contains molecules from which a suspicion of use of banned substances has been deduced."
The International Skiing Federation did not confirm or deny the retired athlete tested positive.
Estonian Olympic team spokesman Sven Sommer told Reuters in Sochi he was unaware of any positive test.
Smigun-Vaehi said: "All of these samples were also analyzed in depth eight years ago, and all have confirmed one thing - I have not used banned substances.
"All of these samples were clean and were expected to be, because I have never used any banned substance."
The International Olympic Committee is retesting samples going back eight years with newer methods and looking for substances that at the time could not be traced.
It has said the retesting of the Turin samples had been done but that no information would be provided until the whole process was complete.
That would happen after the end of the Sochi Olympics in Russia, which start later on Friday, it has said.
(Reporting by Karolos Grohmann, Additional reporting by David Mardiste; Editing by Peter Rutherford)
