The Hoops striker was due to appear before a hearing at Hampden on Thursday to answer a charge of "not acting in the best interests of Association Football by singing in public about Hearts in administration".
He was also due to answer a further charge of "bringing the game into disrepute" by allegedly singing songs of an offensive, racist and/or discriminatory nature racist nature about former Jambos star, Rudi Skacel.
The SFA had received Crown Office approval to proceed with their case against Griffiths, despite the fact Police Scotland's inquiry into the incident - which is alleged to have taken place in the Roseburn Bar, Edinburgh before a Hearts v Hibs match on March 30 - was ongoing.
However, Griffiths' legal representatives have today requested the SFA proceedings be postponed to allow these external investigations to be concluded.
After camera phone footage emerged, the 23-year-old was originally charged by the SFA on the single count of not acting in the best interests of Association Football by singing in public about Hearts in administration.
Celtic held their own investigation into the alleged incident and fined the player four week's wages.
However, within days, more footage from the Roseburn Bar prior to the capital derby - which Griffiths also attended - emerged, and it is alleged to show Griffiths participating in a song which referred to Skacel as "a refugee".
The police and Celtic instigated separate investigations into these allegations, and the SFA also served a further Notice of Complaint which included the more serious charge regarding the singing in public a song of an offensive, racist and/or discriminatory nature.
Celtic manager Neil Lennon has stated he expects the player to still be at the club next season, and brought him on as a substitute during Saturday's 3-3 draw with Motherwell.
Griffiths got a mixed reception from the Celtic support when he took to the field in the second half, and cupped his hand to his ear as he celebrated scoring his team's third goal.
If found guilty by the SFA, he faces a lengthy ban.
But, due to the postponement of the hearing, any suspension will not be served until the start of next season.