Griffiths had already been charged last week with not acting in the best interests of football, when video footage showed the 23-year-old singing a song about Hearts in administration.
And the notice of complaint has now been revised by the Scottish Football Association after an SFA compliance officer watched fresh video footage which emerged over the weekend.
This appeared to show the Scotland international singing in a pub with Hibernian fans as they chanted a derogatory song about former Hearts player Rudi Skacel.
Griffiths has now been issued with a more serious charge and the SFA disciplinary hearing has been set for April 24.
The forward used to play for Hibs and was filmed with fellow supporters prior to watching the Edinburgh side lose 2-0 to local rivals Hearts at Tynecastle on March 30.
When footage emerged last week showing the fans singing "Hearts are going bust", Celtic manager Neil Lennon warned Griffiths that the transgression was "his one strike".
On Monday Celtic stated that they took the new allegations "extremely seriously" and Police Scotland said they had launched inquiries into allegations of "racist chanting by a 23-year-old Scottish Premier League footballer".