The national side could face sanctions for breaching two counts of the governing body's disciplinary code.
The banner read 'Las Malvinas son Argentinas', which translates as 'the Falkland Islands belong to Argentina', with the players holding it in front of them in an act of support before kickoff.
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The actions of the national side are in direct breach of two counts of FIFA's disciplinary code and the governing body has now confirmed it will open an investigation.
A statement read: "The chairman of the FIFA disciplinary committee has decided to open disciplinary proceedings [against Argentina] based on an apparent breach of art. 60 of the FIFA stadium and security regulations (‘prevention of provocative and aggressive actions’) and art. 52 of the FIFA disciplinary code (‘team misconduct’).”
Argentina's FA will have the opportunity to explain its stance and provide any footage or material to support the case.
Alejandro Sabella's side opens its World Cup 2014 campaign with a clash against Iran at the Estadio do Maracana on Sunday.