The man was arrested by detectives in Dublin this week under gangland legislation in relation to the murder of the 17-year-old boy.
He was questioned at a north Leinster garda station and senior sources say he is suspected of having a "peripheral role" in the high-profile murder.
A garda spokesman said the man has been released without charge and a file will now be prepared for the Director of Public Prosecutions.
In total, 13 people have now been arrested as part of the murder inquiry, with three men charged before the courts.
Mulready-Woods was murdered and dismembered at a house in Drogheda as part of a feud involving two gangs in the Co Louth town.
Partial remains, including his limbs, were found in a bag in Moatview Gardens, Coolock, on January 13 last year.
Two days later, his head and hands were found in the boot of a burnt-out car at Trinity Terrace near Ballybough in Dublin.
The boy's torso was found during a search of waste ground at Rathmullan Park in Drogheda, last March 11.
Officers were acting on "key intelligence" in the search operation. His family later buried the torso with the rest of Mulready-Woods's remains.
The torso remains were found hidden in overgrown bushes in a ravine and also under soil at the site.
Last month, two men were sent for trial to the non-jury Special Criminal Court in relation to the murder.
Mr Justice Tony Hunt made the formal orders after the accused, Paul Crosby (25) and Gerard Cruise (47), were sent forward from the district court.
The cases against both Mr Crosby, of Rathmullan Park, Drogheda, Co Louth, and Mr Cruise, with one address at Rathmullan Park and another in Dublin 1, were adjourned.
They are both charged with the murder of Mulready-Woods at a house in Rathmullan Park, Drogheda, on a date unknown between January 12 and 13, 2020.