The father of two was killed in his home in Buncrana, County Donegal, in February 2012.
Republican Action Against Drugs (RAAD) admitted responsibility for the murder. Mr Allen's family have always denied claims he was a drug dealer.
He was the first man to be murdered by the vigilante group.
The suspect was arrested on Monday morning and is being held at Buncrana Garda Station.
Gardai said the man was arrested in Burnfoot, County Donegal.
Irish police have arrested a man in his 30s in connection with the murder of Londonderry man Andrew Allen.