Police Scotland are investigating the matter after screenshots posted on social media, allegedly from Griffiths’ Instagram account, appeared to show the 30-year-old striker exchanging messages with the teenager, who cannot be identified for legal reasons.
Celtic have also launched their own probe and Griffiths has been sent home from the club’s pre-season training base in Wales.
A club spokesman told The Scottish Sun: "We have been made aware of online comments concerning Leigh Griffiths. The club will now look into this matter carefully.
“Leigh has left the Club’s training camp as we do this.
“It would not be appropriate to make any further comment at this time.”
Griffiths signed a one-year contract extension at Celtic last week and has made 261 appearances for the Parkhead club, scoring 123 goals.
A Police Scotland spokesman said: “We have been made aware of social media content. We are making enquiries and assessing for criminality.”