FIFA said Argentina had potentially breached rules regarding “offensive behaviour and violations of the principles of fair play” and “misconduct of players and officials”.
World football’s governing body is also investigating the Argentinian FA over breaching media and marketing regulations.
Croatia are being investigated for potential violations of “discrimination” and “order and security at matches” rules.
Players appeared to sing a song with fascist connotations following their third-place play-off victory over Morocco.
Defender Dejan Lovren defended himself and his teammates, recently telling AFP it was “a patriotic song which relates to my country, which means that I love my country”.