Leigh Griffiths was sent home from Celtic's pre-season training camp after police began a probe into online activity.
Celtic are also investigating claims that Griffiths sent inappropriate messages to a 15-year-old girl on social media.
A Police Scotland spokesman said: "We have been made aware of social media content. We are making enquiries and assessing for criminality."
Griffiths did not feature in Ange Postecoglou's first friendly game in charge of the club as Celtic beat Sheffield Wednesday 3-1 in Newport on Wednesday afternoon.
A Celtic spokesperson told several media outlets: "We have been made aware of online comments concerning Leigh Griffiths. The club will now look into this matter carefully.
"Leigh has left the training camp as we do this.
"It would not be appropriate to make any further comment at this time."
Celtic took up a one-year option on the 30-year-old striker's contract last week after his Parkhead future had been in doubt.