Both the victim and the man in custody are originally from Leixlip.
A 40-year-old man is still being questioned by gardaí in connection with the murder of another man in Kilcock yesterday afternoon.
The 50-year-old victim died violently at an apartment on School Street in the town.
He was attacked and stabbed to death sometime between 3pm and 4pm yesterday afternoon.
A man was arrested at the scene and is still being detained in a Garda station in Kildare.
He can be questioned for up to 24 hours before he must be either charged or released.
Both the victim and the man in custody are originally from Leixlip.
The scene remains sealed off for a forensic examination which will continue today.
The scene at School Street was cordoned off.
A post-mortem examination will be carried out today on the mans body at Naas General Hospital by State Pathologist Sally Ann Collis.
Gardaí said they are following a definite line of inquiry and are not looking for anyone else at present.
An incident room has been established at Leixlip Garda station and a senior investigating officer and family liaison officer have been appointed.
Members of the Kildare County Fire Service attended the scene.
Gardaí are seeking to establish a motive for the fatal stabbing and have issued an appeal to anyone with information to contact them.
Garda specifically want to speak to road users who were in the School Street area between 3pm and 4pm yesterday afternoon.
They are also seeking anyone that may have dash cam or mobile phone footage to come forward.
Anyone with information is asked to contact Leixlip Garda Station on 01 6667800, the Garda Confidential Line on 1800 666 111, or any Garda station.
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