The medal was awarded to an unnamed member of the yacht Hera, which sailed to victory in a unique race on the Clyde.
The solid silver prize was designed by Bertram MacKennal and features an athlete crowned by maidens on one side and St George and the Dragon on the reverse. It has a reserve £3000 to £5000 for the auction at McTear's in Glasgow on March 4.
Although the majority of the competitions were held at Cowes, Olympic organisers agreed to hold the 12 Meter Yacht Race out of Hunters Quay, Dunoon, to avoid other racing boats.
Captained by Sir Thomas Glen-Coats, of the Coats textile family in Paisley, Hera was crewed entirely by members of the Royal Clyde Yacht Club. Hera later disappeared off the coast of Argentina in 1950.
McTear's managing director, Brian Clements, said: "This is a fascinating piece of sporting history that illustrates Scotland's links with the Olympic Games."