Inland Fisheries Ireland said the pink salmon, which are of Pacific origin, were found in rivers in Counties Galway, Mayo and Donegal.
The fishing board said it was concerned about the impact the fish may have on Ireland's Atlantic species.
The pink salmon was also found earlier this month in Scotland.
Pink Salmon, also known as humpback salmon, originate from the west coasts of the United States, Canada and northern Asia.
The fish are a favourite prey of North America's grizzly bears.
A potentially invasive species to the UK, the salmon may be related to fish introduced to the Barents Sea in Russia in the 1950s.
The species can be identified by the following characteristics:
However, Dr Greg Forde, head of operations at Inland Fisheries Ireland, said "it seems unlikely that these fish made a migration due to their small size".
He said the appearance of the species was a "mystery".
"We are appealing to the public, and the angling community in particular, to be vigilant and to report any catch of pink salmon to Inland Fisheries Ireland," he added.
A non-native species of salmon has been found in rivers along the west coast of Ireland, causing concern among Irish fishing authorities.