Travelling supporters fired the flare on to the track around the pitch during the Group A encounter on October 15.
They also let off smoke bombs during the match - won 2-0 by Scotland - but the SFA could be punished along with the Croatian federation because it was responsible for security at the game.
The 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 told Press Association Sport: "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."
Press Association Sport contacted the SFA for its response, but they declined to comment at this stage.