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.

Vicki McNelly, 29, thought she heard the baby moving when she used the Doppler kit but her daughter was stillborn the following day.
Manufacturers say the kits are safe and should not be linked to stillbirths.
Experts who have been "specially trained" regularly use the monitors but discourage the use of them at home.
Mrs McNelly, from Mortimer near Reading, is calling for the Doppler devices to be banned.
She had used the kit - which can be bought over-the-counter from about Â£25 - in June 2015 to help her husband bond with their baby.
However, after waking and "feeling something was wrong" in the middle of the night, she used it to check for a heartbeat and movement.
"Because I heard something, I convinced myself I must be okay and that everything would be fine," she said.
"If the Doppler wasn't in the house I would have only been able to rely on my own instincts. I think the Doppler gave me a false sense of security."
Mrs McNelly said a hospital sonogram revealed her child, who she had named Evie, had died in the womb.
Dr Alison Wright, Vice President of the Royal College of Obstetricians and Gynaecologists, said she "strongly discourages" the use of Dopplers at home.
"These devices can cause huge anxiety among pregnant women if they are not able to hear their baby's heartbeat and therefore understandably worry until they can see their doctor or midwife," she said.
"Also, potentially, women may be falsely reassured as hearing a heartbeat is not necessarily an indication that it is well with the baby.
"Unlike doctors and midwives who are specially trained to use foetal heart monitors, women who use Dopplers themselves may easily mistake their own heartbeat for their baby's."
Mrs McNelly has now joined stillbirth charity Kicks Count to call for the devices to be banned - with a petition reaching more than 11,000 signatures.
CEO of Kicks Count, Elizabeth Hudson, said Dopplers "create a barrier between the mum and seeking medical help".
She said many brands were marketed to expectant mothers, but should only be used by trained professionals such as midwives and doctors.
"Women are using Dopplers and being reassured by them, and unfortunately that leads to missed opportunities to save babies who may be in distress," Ms Hudson added.
The BBC contacted several Doppler manufacturers, which said their devices should not be used as a substitute for professional medical care.
A non-native species of salmon has been found in rivers along the west coast of Ireland, causing concern among Irish fishing authorities.
[NEXT_CONCEPT]
A grieving mother has warned pregnant women not to use a home foetal listening device that gave her "false reassurance" her unborn baby was alive.