The warning comes as gardai step up their investigation into the murder of notorious mobster Kelly. He was shot three times in the chest with a handgun as he walked towards his home at Furry Park Road in Killester on Tuesday afternoon.
Sources say that the new threat against Enright (32) could be linked to his close friendship with a member of the Kelly family.
The death threat against Enright emerged just days after Eamon Kelly's older brother Matthew (68) was also warned about threats against him.
Sources say that the Real IRA are behind the threats and that the campaign of terror is being directed by associates of well known Northern Ireland dissident Republican Colin Duffy.
A source explained: "What is going on is very serious -- death threats are being made all over the place. And as you can see from what happened Eamon Kelly -- these threats need to be taken very seriously."
Their latest target Sean Enright -- who dabbled in music promotion in the past -- made a miraculous recovery after being shot six times by Alan Ryan's RIRA crew outside his girlfriend's home in Clonsilla, west Dublin, in January 2011.
Originally from the Cabra area, Mr Enright is a father of two who spent over a week in James Connolly Memorial Hospital after being shot.
Meanwhile, a notorious Real IRA suspect from Bluebell in Dublin's south city continues to be questioned today at Clontarf Garda Station after his arrest close to the scene of Kelly's shocking gun murder.
The 33-year-old criminal is being questioned about illegal possession of a firearm and membership of an illegal organisation.