Crimelord Dunne was shot dead in a packed pub in Cabra on Dublin's northside in April 2010.
The suspect, who is in his 20s, was today being detained in Mountjoy Garda Station and can be questioned for up to a week.
This morning's arrest brings to 11 the number of arrests made in relation to the murder in the Fassaugh House pub.
Gardai believe that Dunne was murdered by a gang of north inner city criminals who had strong links to international crime godfather Christy Kinahan.
Dunne was sitting next to his then 17-year-old daughter in the Fassaugh House pub on April 23, 2010 when two gunmen entered and fired up to a dozen shots.
One of the men walked up to Dunne and shot him a number of times in the back of the head and fired more shots after Dunne had hit the ground.
The second gunman, who was armed with a revolver, stood just inside the pub door, ready to shoot anybody who tried to intervene.
Two other men waited outside the pub in a VW Passat getaway car which was later found close to the pub.
Dunne had been in the pub to celebrate the 38th birthday of his close pal John Fairbrother.
Last week, one of Dunne's closest associates, Joe Warren (30) from Ballymun, was jailed for a total of 11 years for possession of ammunition charges and for conspiracy to rob a cash-in-transit van at Celbridge, Co Kildare, in November 2007.
At the time of his murder, Dunne was facing the same conspiracy charge and was also due to face sentence for drug dealing offences.