Their announcement followed reports that a severed pig's head had been placed in the locker of forward Kenwyne Jones as a practical joke.
The incident has been mentioned extensively on social media, Stoke defender Brek Shea having tweeted a picture of himself holding the pig's head aloft.
And it has been reported by the Daily Telegraph that Jones, furious about the prank, threw a brick through the windscreen of team-mate Glenn Whelan's car in retribution.
Stoke released a statement on Friday which read: "The club takes seriously reports of an incident at our training ground this afternoon.
"A full internal investigation will be carried out and those responsible for any unacceptable behaviour will be dealt with in accordance with the club's disciplinary procedures."