He was one of three men and a woman who are being questioned at various north Dublin stations. Kelly was gunned down close to his home in Killester last Tuesday evening.
The IRA suspect is from Tallaght and is in his 30s. It is understood that he has been a major target of the garda's Special Detective Unit for almost a decade.
He was previously convicted of IRA membership and served a four-year sentence for the offence at Ireland's highest security prison in Portlaoise.
The suspect was one of six people picked up across the capital on Saturday after detectives got key information from an informer about Kelly's murder.
A man and a woman were released without charge yesterday morning and a file is being prepared for the DPP in relation to them.
On Friday night, Sean Connolly, 34, of Bernard Curtis House in Bluebell, south Dublin, was charged with the murder.
He was also charged with possession of a Glock semi-automatic pistol with intent to endanger life and membership of the Real IRA.
Connolly will reappear before the three-judge non-jury Special Criminal Court via video link on December 20.
It is understood that he is being kept in a special segregation unit of Portlaoise Prison.
Sources say that gardai have been working on the theory that Kelly's murder was sanctioned in Northern Ireland by new terror faction, The IRA. This is an amalgamation of the Real IRA, Republican Action Against Drugs and former members of the Provisional IRA.
Apart from ordering the murder of Kelly, the IRA leadership in the North has demanded 'a major clean-up' within their own dissident Republican ranks which has seen a former close associate of slain RIRA boss Alan Ryan being kneecapped.