The discovery was made by a member of the public out walking on Arranmore Island at the weekend.
Photographs of the whale carcass were shared on Facebook by Arranmore Blue Ferry.
"What a beautiful creature - this is so sad," said one woman.
"It's such a shame to see one of natures great gifts end up like this," added another.
The International Union for Conservation of Nature lists fin whales as an endangered species.
After the blue whale, the fin whale is the second largest mammal on Earth.
Fin whales can take up to 30 years to reach full physical maturity (maximum size) and may live for 90 years or longer.
The International Whaling Commission lists the fin whale as a protected species.