Mobile phone footage passed to the Sunday Mail appears to show the footballer singing a derogatory chant about former Hearts player Rudi Skacel.
The 23-year-old was allegedly filmed in Edinburgh's Roseburn Bar before Hearts played Hibernian on March 30.
Griffiths, a former Hibs player, has already been fined by Celtic and faces disciplinary charges by the Scottish Football Association after he was filmed singing about Hearts' financial problems at the same pub last Sunday.
A Police Scotland spokeswoman said: "Following an article in a Sunday newspaper alleging racist chanting by a 23-year-old Scottish Premier League footballer, inquiries are being initiated by Police Scotland."
Celtic were unavailable for comment.