The nest, which has been used by a pair of golden eagles for seven years, is near the island capital, Tobermory. Plastic items were placed in the nest stopping birds from breeding.
Inspector Julie McLeish, of Oban police station, said: "Sticks and plastic items had been placed in the nest."
Ian Thomson, head of investigations at RSPB Scotland, added: "From what we can surmise, this was a deliberate attempt to prevent the birds breeding at this site which is very disappointing. "There was too much debris on the nest for them to breed.
"It is a real shame because this was a very successful pair for many years.
A spokesman for Scottish Natural Heritage added: "We would encourage anyone with information regarding this to contact police."