Leigh Griffiths has apologised after the Dundee striker appeared to kick a flare into a stand of spectators during Wednesday's 2-0 defeat by St Johnstone.
Dundee said "a smoke generator, amongst other items, was thrown onto the park by the visiting supporters" after the opening goal in the League Cup tie.
Police say "enquiries are ongoing".
"It was regrettable that the pyrotechnic ended up back in the stand as my intention was just to remove it from the pitch," said Griffiths.
"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."
A Police Scotland 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."
Scotland forward Griffiths returned to Dundee on loan from Celtic late last month, having originally played for the Tayside club between 2009 and 2011.