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.

The barrister and master of Clare College Cambridge will remain a party member but will sit as a crossbencher.
He told the Times Jeremy Corbyn's proposals were "terribly damaging".
It comes five days after former junior health minister Lord Warner resigned the Labour whip, saying the party did not have a "hope in hell" of winning power under its new leader.
Lord Grabiner said Labour was now in "disarray" and that he could not "square [staying] with my conscience".
He added: "I have nothing in common whatever with Mr Corbyn and I don't believe we are ever going to win an election."
He also said he was particularly concerned about John McDonnell's appointment as shadow chancellor.
"I am concerned with the economic stuff. I am really concerned with the shadow chancellor," he declared.
Former Labour cabinet minister Lord Mandelson has also criticised Mr Corbyn. Speaking on the BBC's Week in Westminster programme, he said the Labour leader was not "growing into the job at all".
Mr Corbyn was not showing "any professionalism in his leadership of the Labour party", and had made poor choices in his appointment of senior staff in his team, he said.
A Labour spokesman said of the peer: "We welcome Tony's continued membership and support of the party.
"We know he has been increasingly busy and less able to attend the Lords to participate in House business and we of course understand his decision to relinquish the Labour whip".
The spokesman also said Lord Grabiner had not voted in the Lords since 2013.

Tests by Southampton University found people's walking patterns - their gait - are so different they could be used to identify individuals.
Researchers used a multi-biometric tunnel with 12 synchronised cameras to capture and translate 25 subjects' gaits to build unique 3D images.
It is hoped the technique could be used for a variety of purposes, including security monitoring at airports.
'Extreme clothing changes'
Darko Matovski, who led the investigation, said: "We have shown for the first time that gait can be used as a reliable biometric trait over time."
The team believes the technique could be used in airport immigration halls where "a simple corridor with cameras" would be enough to identify large flows of people.
Mr Matovski, from the university's school of electronics and computer science, added: "A bank robber may wear a mask so you can't see his face, wear gloves so you can't get fingerprints, wear a hat so you can't get DNA evidence - but he still has to walk into the bank and you can identify him from the walk."
With almost 2,000 walking sequences recorded in a database, Mr Matovski claims a 95% success rate.
Gait can also be measured at a distance - an advantage over other forms of biometric identification.
However researchers found that "extreme changes" in clothing can affect recognition levels.

City had been due to face a winding-up petition on Monday, but Cox told BBC Radio Oxford it will not now be heard.
A judge could have passed a winding-up order that would have liquidated the 134-year-old club.
Oxford are next to bottom in National League South, having won only one of their eight games so far this season.
It has been a turbulent few months for the club, with former club president Thomas Guerriero jailed for fraud in May and managing director Colin Taylor found dead at the club's stadium in July.
Celtic striker Leigh Griffiths has pleaded not guilty to accusations he took part in offensive chanting at a pub in Edinburgh last year.
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Lord Grabiner has become the second peer in recent days to resign the Labour whip in the Lords.
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Criminals could be tracked down by the way they walk, a study has claimed.
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Oxford City chairman Brian Cox has confirmed that a pending High Court hearing has been called off after the club paid an outstanding tax bill.