The FAI have been fined 5,000 Swiss Francs (€4,700) after the Republic of Ireland wore an Easter Rising symbol on their jerseys during last March's friendly clash with Switzerland.
Ireland players wore the symbol at the Aviva Stadium to mark the 100th anniversary of the Rising.
However, the gesture was called into question by British MP Damian Collins, who subsequently asked FIFA to clarify why the Irish were permitted to wear a symbol commemorating the Easter Rising, while the England, Wales and Scotland football teams were banned from wearing poppies.
"I have asked FIFA to clarify the issue over shirts worn by the Republic of Ireland because that appears to be an absolutely classic example of leniency being shown to other countries," he told the BBC.
FIFA have responded by fining Ireland, with the English FA also being punished with a fine of 45,000 Swiss Francs (€42,000) after England players defied the poppy ban by wearing them in the 11 November World Cup qualifier against Scotland.
FIFA said the association had been fined over "the display of a political symbol on the shirt".
The Scottish Football Association and the Football Association of Wales were fined 20,000 Swiss Francs (€18,700) and the Irish Football Association 15,000 Swiss Francs (€14,000) for related offences.
The FA announced its intention to appeal the fine.
England and Scotland players wore armbands displaying poppies during their World Cup qualifier at Wembley.
A number of other Armistice Day tributes also took place prior to the match.
FIFA had warned the associations the displaying of political symbols could be punishable ahead of the game, but the FA and SFA both went ahead with plans for players to wear poppies.
The FAW and IFA, for Wales and Northern Ireland matches against Serbia and Azerbaijan respectively, decided on plain black armbands for players but were still punished for displays of the poppy around the stadium.
These included the wearing of poppies by players.
A statement from FIFA read: "England has been fined CHF 45,000 for several incidents in the framework of the England v Scotland match, including the display by the host association, the English team and spectators of a political symbol and several cases of spectator misconduct.
"Scotland, as the visiting association, has been fined CHF 20,000 for the display of the same political symbol and cases of misconduct committed by its own group of spectators.
"Wales has been fined CHF 20,000 and Northern Ireland CHF 15,000 in relation to several incidents, including the display of political symbols in the context of the Wales v Serbia and Northern Ireland v Azerbaijan matches."
The associations are now awaiting the full written verdicts from FIFA. The Northern Irish governing body says it will seek legal advice before considering its response.
A statement read: "The Irish FA is disappointed that the FIFA disciplinary committee has reprimanded the association and issued a fine in relation to acts of remembrance at the Northern Ireland v Azerbaijan match on November 11.
"The Irish FA will examine the full written submission when it is released and will take further legal advice before deciding on a future course of action."
The SFA echoed its Northern Irish counterpart in emphasising its unhappiness with the punishment.
It said in a statement that it was "disappointed by the outcome of the FIFA disciplinary committee" and would "await the written reasons from the committee before considering the appropriate next steps".
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