The Celtic striker was due to face two charges in a Hampden hearing on Thursday after he was filmed in a pub full of Hibernian supporters before attending last month's Edinburgh derby.
An SFA statement read: "At the request of his solicitor, the principal hearing date relating to the notice of complaint issued to Leigh Griffiths on Wednesday, April 9 has been adjourned until Thursday, May 22 to allow for the conclusion of the ongoing criminal investigation by Police Scotland."
Griffiths was initially charged by the SFA with not acting in the best interests of football by ''singing about Hearts in administration'' after being caught on camera singing "Hearts are going bust" - an act that saw him fined by Celtic.
The club and Police Scotland then launched an investigation after fresh footage emerged during which the Scotland international is seen apparently singing and dancing as Hibs fans sing a song which refers to former Hearts player Rudi Skacel as a "refugee".
The SFA followed that with an updated charge of bringing the game into disrepute by ''singing in public a song of an offensive, racist and/or discriminatory nature''.
Celtic manager Neil Lennon - who previously stated he had a "zero tolerance" approach to racism - said last week that he was confident Griffiths would remain a Celtic player following the conclusion of the club's probe.