Visiting supporters fired the device onto the track around the pitch during the Group A match on October 15, which Scotland won 2-0.
The Croatian FA is likely to be punished for the behaviour of their fans, but the Scots could also be fined because they were responsible for match and stadium security.
England's Football Association is similarly set to be punished following the match with Poland at Wembley after Polish supporters set off multiple flares during the game.
The Hampden incident was included in the match report sent to FIFA by Romanian referee Ovidiu Hategan and a FIFA spokeswoman confirmed that the game's global governing body was now investigating.
She said: "We can confirm disciplinary proceedings have been opened against the SFA and the Croatian Football Federation for incidents reported during the preliminary competition match of the 2014 FIFA World Cup Brazil between Scotland and Croatia on October 15.
"As the proceedings are ongoing we cannot comment further."
The SFA is yet to comment on the development.