A video posted on social media shows the Dundee striker launching the flare back into the stand housing St Johnstone fans after it had been thrown onto the pitchside during Wednesday’s Premier Sports Cup quarter-final tie at Dens Park.
The on-loan Celtic striker, who ended up on the losing side as the hosts crashed to a 2-0 defeat, was reportedly reacting to abuse from the visiting support when he booted the pyrotechnic back into their section.
While no police complaints have been filed at this stage, a statement from the force confirmed that an investigation is underway.
The police spokesperson said: "We are aware of an incident involving a small number of smoke devices at Dens Park, during the match between Dundee and St Johnstone Football Clubs on Wednesday, 22 September.
"There were no injuries and no complaints have been made to police at this stage.
"Enquiries into the matter are ongoing."
Match officials took no action against Griffiths at the time, but he could yet face disciplinary action with the SFA likely to conduct their own review into the incident before deciding whether any punishment is necessary.
Dundee are due to face Rangers in a Scottish Premiership fixture at Dens Park on Saturday but Griffiths now faces an anxious wait over whether he will be available for the match.
The 31-year-old has yet to score in three appearances for the Dark Blues since returning to his former club on a season-long loan on transfer deadline day.