The discovery was made at around 3pm at a house near the village of Irishtown in the Claremorris region, after the alarm was raised by an acquaintance of the family.
The man is believed to be in his 70s and the woman in her 60s. They were named locally as Tom and Kitty Fitzgerald and were understood to have been very well known in the area.
A man in his late 30s was also found at the scene with serious head injuries. He was taken to University College Hospital Galway.
The scene was preserved pending a full technical examination.
The State pathologist was informed and was en route to Mayo to carry out the autopsies last night.
Gardaí have appealed for anyone with information about the incident to come forward.
Meanwhile, gardaí are not looking for anyone else in connection with the discovery of two bodies in Naas, Co Kildare, on Monday.
A couple in their 70s, named as Joe and Maureen Bradley, were found dead in their home in Ashfield Park Estate in the town.
The bodies were discovered at around 11.30am. The house was sealed and the scene was examined by the state pathologist.
Autopsies were due to be carried out at Naas General Hospital which will determine the direction of any subsequent investigation, but it is understood the incident is being treated as a tragedy.
No foul play is suspected and gardaí are not treating the deaths as suspicious.