Father-of-three, Martin O'Rourke, 24, died after he was shot several times outside a pub in the Sheriff Street/Oriel Street area at about 12:30 local time on Thursday.
It is understood the murder was a case of mistaken identity.
A handgun was found in a bin a short time after the shooting.
Mr O'Rourke tried to run but was shot several times by a gunman dressed in dark clothes, who then cycled away.
The gun is now undergoing ballistic tests but is believed to be the murder weapon. Police have also recovered a black bicycle.
The scene of the shooting remains cordoned off.
RTÃ‰ reports that it is the fifth murder as part of a feud between associates of Gary Hutch, who was shot dead in Spain last year, and David Byrne, who was connected to the Kinahan international drugs cartel based in Spain.
Police in the Republic of Ireland believe they have recovered the weapon used in the murder of a man in Dublin.