Gareth Hutch was shot dead at about 10:00 local time on Tuesday at the Avondale House flats on North Cumberland Street where he lived.
Mr Hutch was the nephew of Gerard Hutch, the man known as 'The Monk'.
On Tuesday evening, a 29-year-old man was arrested after he handed himself into gardaÃ­ (Irish police) and is being held at Mountjoy Garda Station.
He can be detained for up to seven days under anti-gang legislation.
Police have cordoned off the scene for a forensic examination.
The killing is believed to be connected to an ongoing feud between two criminal gangs in the city.
Six people have died since February as a result of a violent dispute between the Hutch and Kinahan gangs.
Last week, Patrick Hutch became the first man to be charged with one of the murders.
He is accused of killing David Byrne in a shooting at a boxing weigh-in event at the Regency Hotel in Dublin in February.
The murder of Mr Hutch's brother Gary in Spain last year is believed to have been the first death in the feud.
A man has been arrested following a fatal shooting in Dublin's north inner city.