The 22-year-old Hibernian striker was reportedly stopped by security guards in an Edinburgh branch of Tesco.
Lothian and Borders police have confirmed that a 22-year-old man was arrested and charged with shoplifting.
Hibs confirmed in a statement that Griffiths was at the centre of the allegations: "The club is aware of an alleged incident which took place on Saturday afternoon involving the player. This is now a police matter."
But Griffiths himself - who is on loan from Wolves and made his Scotland debut last year - maintained via Twitter that it had all been a mistake on the part of the store's security staff.
“Not been caught shoplifting at all! “Lot of bull****! So you’s can all take your rumours to f***!” he Tweeted.
"Got taken to the back, asked about it, looked on CCTV and I was away, simple as that!"
He later added: "Iv been caught shoplifting but I'm tweeting? Pretty sure I'd be in a cell??? Think about it! #hugemisunderstanding".