Gigalum, which lies just off the south-eastern tip of Gigha, is being marketed at offers over £550,000 with estate agents Rettie saying it has potential, subject to planning consent, for a renewable energy scheme or more homes.
The only building on the island is Gigalum House, which was built in 1980 and has a unique structure with a central octagonal core for the living space and four wings housing bedrooms and the kitchen.
Rettie said that while the home had been regularly maintained, it offered "rustic but charming holiday accommodation".
The island itself spans just over 19 acres, with a jetty providing access to the Isle of Gigha and the neighbouring island of Cara, and pathways link the pier to the house.
The estate agents described it as a "spectacularly sited island with wonderful surrounding seascape and far reaching scenic views to Gigha, Kintyre, Jura, Islay and Northern Ireland".
They added: "There is an opportunity of using modern technologies to upgrade the services if desired.
"But in the meantime the house provides rustic and charming accommodation to enhance the memories and character of any stay.
"There may also be the opportunity, subject to planning consent, to extend the house, develop renewable energy sources and possibly build additional dwellings if desired.
"Over the years the island of Gigalum has been home to many camping experiences as well."