The 24-year-old is alleged to have sung an offensive song while in a pub in Roseburn Terrace ahead of the Hearts - Hibs derby on 30 March last year.
The player is charged under the Offensive Behaviour at Football and Threatening Communications Act.
He made his plea to Edinburgh Sheriff Court by letter.
The case was continued until September, with Griffiths due to stand trial in October.
It is alleged the former Hibs player, who is also a supporter of the club, sang a song with offensive lyrics which was likely to incite public disorder.
Celtic striker Leigh Griffiths has pleaded not guilty to accusations he took part in offensive chanting at a pub in Edinburgh last year.