The 11 month old was found at an apartment at Park Place shortly before 6 o’clock on Sunday evening, when it’s believed his mother returned from work.
A man found at the scene remains in hospital in Tralee.
A post mortem was carried out yesterday on the 11 month old, named locally as baby Karol Rozycki, but Gardaí are withholding the results for operational reasons.
Superintendent Flor Murphy says the scene at Park Place on Upper High Street, Killarney remains sealed off, and the investigation is being treated as sudden death.
A man in his 30s, believed to be a relative of the infant and from Poland, was taken from the scene on Sunday to hospital in Tralee; Gardaí say he sustained serious injuries and will be receiving treatment for some time.
Superintendent Murphy is making a direct appeal to people who were in or around the Park Place Apartments in Killarney last Sunday between 1 and 6pm, and to anyone who may have information on the incident.