A World Cup record 18 yellow cards were shown as Argentina defeated the Dutch 4-3 on penalties Friday after a 2-2 draw at Lusail Stadium.
The game featured multiple mass confrontations and heated exchanges as the Dutch came back from two goals down to force extra time.
The charges against the Argentina football federation relate to player and staff misconduct and "order and security at matches," FIFA said in a statement.
The Dutch also face an investigation into the team's behavior.
The fiery game featured two late goals by Netherlands’ Wout Weghorst, which cut Argentina's two-goal lead and forced extra-time.
Extra-time failed to produce any more goals, and the second quarterfinal of the night went to penalties.
Messi praised his team's resilience - but was furious with Spanish referee Antonio Mateu Lahoz, especially at his awarding of the free-kick that gave Weghorst the chance to equalize.
"We knew how to suffer when it was our turn, but we got through to the semifinals. It's beautiful, something impressive," Messi said speaking after the game Friday.
"I don't want to talk about the referee, because they immediately reprimand you or sanction you, but I think people saw what happened.
"FIFA has to review that -- it can't give a referee like that a match of this importance, when they're not up to the task.," Messi said.
