The 24-year-old has now been charged by the SFA with "singing in public a song of an offensive, racist and/or discriminatory nature" and subsequent contraventions of disciplinary rules 79 and 86, with a principal hearing date of April 24 set for the case.
Griffiths is also the subject of an ongoing police investigation and has already been disciplined internally by Celtic.
The ex-Hibs hitman has been forced to apologise to Hearts for singing in public about the Gorgie club going bust and former Jambo Rudi Skacel being a refugee, with Celtic gaffer Neil Lennon also warning Griffiths about his future conduct.
McGarvey said: "Leigh Griffiths has to learn to screw the nut. He is a Celtic player now and he has certain responsibilities to the club and everything it stands for.
"I have nothing against former players going to watch their old clubs as I was at Celtic and went to watch St Mirren plenty. But I did not go singing songs about other players or clubs and Leigh Griffiths is now in the last chance saloon with Celtic and must learn from this.
"He has put Neil Lennon in a very difficult position and that can't be allowed to happen again."
But McGarvey is crossing his fingers Griffiths will not be axed and believes if he survives the rap he can go on to become a Hoops' legend.
McGarvey said: "Griffiths is a fantastic finisher and an absolute stick-on for 20 goals plus a season.
"I have no doubt that he will score in the Champions League next season, if he gets the chance, and it would be a crying shame if he is binned.
"He has got to wise up but, hopefully, he has shown enough contrition and the club will allow him the opportunity to turn things around from here."