The Scotland international had earlier declared he had only meant to remove the item from the pitch after it was thrown on following a Saints goal.
A Police Scotland spokesperson said: "Police Scotland can confirm that a 31-year-old man has been charged in relation to culpable and reckless conduct, following an incident at Dens Park, Dundee, on Wednesday, September 22. A report will be submitted to the Procurator Fiscal."
The incident – which happened shortly after Shaun Rooney had scored the opening goal in St Johnstone's 2-0 victory in the Premier Sports Cup quarter-finals – was filmed by a supporter and posted on social media.
Dundee issued a statement on Thursday in which Griffiths apologised for his actions.
It read: "Dundee Football Club and Leigh Griffiths would like to address a regrettable incident which occurred during last night's Premier Sports Cup tie with St Johnstone at the Kilmac Stadium.
"Following the opening goal a smoke generator, among other items, was thrown onto the park by the visiting supporters. This pyrotechnic ended up back in the stand as Leigh kicked it to remove it from the field of play."
Griffiths, who recently returned to Dundee on loan from Celtic, added: "It was regrettable that the pyrotechnic ended up back in the stand as my intention was just to remove it from the pitch.
"Having just lost a goal I was eager to get the match restarted as quickly as possible and I would like to apologise for any distress caused by this action."
Griffiths could also face Scottish Football Association disciplinary action but the police charge could delay that process.
Dundee host Rangers in the cinch Premiership on Saturday.