The 2022 champions were dethroned in New Jersey as Ferran Torres netted an extra time winner to snatch a 1-0 victory for Luis de la Fuente's team at the MetLife Stadium.
However, the post-match celebrations were marred by several violent scuffles between players from both sides, which were picked up by TV cameras and shared across social media in the aftermath.
According to the latest update, FIFA's disciplinary committee will assess the referee's reports and footage from the match before deciding whether to impose sanctions - but a full investigation is on the cards.
The focus is on Argentina midfielder Leandro Paredes who appeared to hit and throw Spain star Gav to the ground alongside an allegation of Nahuel Molina punching Spain captain Rodri.
Argentina coach Roberto Ayala is also accused of pushing Dani Olmo and Argentina's controversial decision to turn their backs to Spain during the trophy presentation will also be looked into as an unsporting gesture.
It's the second time Argentina have faced criticism for their conduct at this World Cup following the team's displaying of a political banner relating to the Falkland Islands after their semi-final win over England.