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.

Its 4G Super Voice enables customers to make calls and send texts using a lower frequency spectrum.
Other networks are looking into introducing the technology, known as Voice Over Long-Term Evolution (VoLTE).
It currently works on only the Samsung Galaxy S5, but recent iPhone handsets will be added in the coming months.
It is being rolled out in:
Three said up to 5.5 million customers would have access to the service by 2017.
Chief technology officer Bryn Jones said: "By the end of the year, one million of our customers will have access to better indoor coverage and be able to use their phones in more places than ever before."
An island in the Menai Strait between Gwynedd and Anglesey is set to go under the hammer.
[NEXT_CONCEPT]
Mobile phone provider Three has launched a UK service it says will improve reception inside buildings and in rural black spots.