It is the third time that the SFA has been forced to cancel a Hampden hearing while it waits for Police Scotland to announce what course of action it will take.
Now it has decided it will not issue a fresh date until Griffiths is dealt with one way or the other by officers.
Griffiths was due to face charges of bringing the game into disrepute and acting against the best interests of football on Thursday after he was filmed in a pub full of Hibernian supporters before attending the Edinburgh derby on April 27.
An SFA spokesman saidt: "Thursday's hearing has been cancelled but no new date will be set until Police Scotland conclude the on-going criminal investigation."
Griffiths was initially charged after being caught on camera singing "Hearts are going bust".
But the SFA notice of complaint was updated after Police Scotland launched an investigation on the back of fresh footage in which the Scotland international is seen as Hibs fans sing a song which refers to former Hearts player Rudi Skacel as a "refugee".