With a guide price of Â£125,000 the sale of Ynys Bach includes the attached Ynys Faelog boathouse - with planning permission to rebuild it.
But anyone interested in buying the island has been warned they would not be allowed to live on it.
It can be accessed through a pedestrian walkway from St Georges Road in Menai Bridge.
Agents Dafydd Hardy said it was an opportunity to buy something unique with fantastic views.
"It would suit a philanthropist with an interest in marine life or maybe an artist would like to sit there painting the Menai Strait," said Mr Hardy.
"I'm looking forward to selling it as it's really interesting."
The lot goes under the hammer on 27 June at 17:30 BST at The Anglesey Arms Hotel, Menai Bridge, Anglesey.
An island in the Menai Strait between Gwynedd and Anglesey is set to go under the hammer.