Duff, 33, who made his debut for the senior team in March 1998 against Czech Republic, captained Ireland in his last appearance for his country in their final Euro 2012 match against Italy after the team failed to qualify for the second round.
"Damien will be missed by us and by Irish fans everywhere. He was immensely skilful and a great example to the players who come after him," Ireland coach Giovanni Trapattoni said in a statement.
Duff started his career in England with Blackburn Rovers before joining Chelsea, where he won two Premier League titles. A move to Newcastle United followed before he returned to London and Fulham.
A tricky, old-fashioned winger, the left-footed Duff was outstanding in the 2002 World Cup, when Ireland last played in the tournament.
Duff told the Football Association of Ireland's website: "I found it very difficult to make this decision, not least for the respect in which I hold Giovanni Trapattoni. I have enjoyed so many good times in the green jersey and want to thank everyone involved, especially the fans for making the last 14 years so special."
He added: "I want to wish Giovanni, Marco and everyone involved with the Irish team every success for the future and will be supporting them every step of the way."