FIFA has so far refused to recognise Ireland's 0-0 draw with Hungary in a June friendly as an official international result because one of the match officials was not on its approved list.
"Mr David Vang Andersen was not on the current FIFA list of referees and this is the reason why they are not recognising the match," the FAI said in the statement.
Media reports in Ireland had suggested that Duff, who ended his 14-year international career when Ireland bowed out of Euro 2012, would be stripped of his cap for that game, leaving him stranded on 99.
But the FAI said the awarding of caps was at the discretion of the national association.
"The Football Association of Ireland has decided that the players who participated in the fixture deserve caps, particularly Damien Duff for the service that he gave to his country," it said in a statement.
"Consequently, the Association has informed Damien that it will recognise his status as having earned 100 caps for Ireland."
The 33-year-old Fulham player, who won England's Premier League twice while at Chelsea, represented Ireland in the 2002 World Cup and 2012 European Championship and scored eight goals during his international career.
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