The Irish foreign minister has said football's governing body should not insist Northern Ireland players carry British passports when going abroad.
FIFA has written to the Irish Football Association to say its officials cannot determine whether footballers with Irish passports can play for NI.
Dermot Ahern said Northern Ireland players should be able to travel on Irish passports if they want.
The SDLP and Sinn Fein have also criticised the FIFA ruling.
Previously, it had been acceptable for players to have a British or Irish passport and Northern Ireland officials had hoped this would continue.
They pointed out that the Good Friday Agreement recognised that all people born in Northern Ireland could opt for British or Irish citizenship.
But the world governing body said the dual passport system presented problems for their match commissioners.
"FIFA sees no alternative but to require players to hold the passport of the national association they are seeking to represent in order to allow the match commissioner to verify their eligibility," said a statement.
"The fact that a player holds an Irish Republic passport does not demonstrate conclusively that he or she is eligible to play for Northern Ireland."
However, Mr Ahern said: "I accept that FIFA and the IFA in order to improve eligibility would have to have some proof of am British passport.
"But from a travelling point of view if a player wishes as he is entitled to under the Good Friday Agreement to produce an Irish passport, in my view that should be accepted at the receiving country."
Sinn Fein's Martin McGuinness also criticised FIFA.
"This is a human right, a national right for Irish citizens to carry an Irish passport," he said.
"If the logic of this ruling was to be followed through by other sporting organisations it could have far reaching ramifications for sport in all of Ireland."
The SDLP's Pat Ramsey said: "It is clear that the Irish government and the IFA must take a stand against what is essentially the sporting marginalisation of half the community in the north.
"This decision is discriminatory, it is damaging, and in the context of the Good Friday Agreement, it is illegal."
The Irish FA's chief executive Howard Wells described FIFA's verdict as unfortunate for Northern Ireland.
"It is a seriously difficult issue to deal with but we have to deal with it," said Wells.
"I need to take stock, and take advice from a number of people as to how we might address it and move forward."