The 2022 champions lost out in New Jersey as Ferran Torres scored an extra time winner to seal a 1-0 victory for Luis de la Fuente's team at the MetLife Stadium.
However, the post-match celebrations were dominated by several violent scuffles between players from both sides, which were picked up by TV cameras and shared across social media.
FIFA have appointed a disciplinary and ethics prosecutor to review the referee's report and post-match video footage before making an assessment over a possible punishment.
A decision is expected to land between August 5th and 10th and Spain will await an update with Dani Olmo the latest to call out the conduct of Argentina's camp in New Jersey.
Olmo appeared to be struck by Argentina coach - and former LaLiga star, Roberto Ayala - in the melee and the Barcelona star has called out the 53-year-old for his version of events.
"Someone who claims to be sorry, but justifies a punch by saying it was a response to something being said, probably isn't sorry at all.
"He's lying. I didn't say anything to him, so I don't need his apology. What truly defines us isn't a mistake, but the courage to acknowledge it.
"When my children, my family, so many fans, and the people of Terrassa watch the match, I want them to be proud of how we competed and won. But above all, of our behaviour, because as players we are role models for children and that carries great responsibility."