According to an English language Turkish news website the man was killed in the Bodrum district of the Aegean province of Muğla on June 3.
The man, believed to be in his 60s, arrived in the area 20 days ago and rented an apartment on Tevfik Street.
Neighbours discovered his body at 2pm on Friday near a bloody knife, and raised the alarm.
Hurriyet Daily News reports that "the body was sent to the forensic medicine institute in Muğla for an autopsy after examinations, which revealed that a struggle between the killer and the victim took place."
Video footage obtained from nearby security cameras shows two men leaving the building.
Turkish police are now investigating the murder.
The Irish Department of Foreign Affairs confirmed that they were offering consular assistance to the man's family.
Bodrum stretches from Turkey's southwest coast into the Aegean Sea and is known for its beach towns and resorts, ancient ruins and vibrant nightlife. It is a popular spot with Irish and British holidaymakers.