Media reports said the angry Trinidad and Tobago international had retaliated by using a golf club to smash the windscreen of a car belonging to Ireland midfielder Glenn Whelan.
"The club takes seriously reports of an incident at our training ground this afternoon," Stoke said in a statement, without giving any details.
"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."
Stoke's U.S. international midfielder Brek Shea posted a picture of the pig's head being held up to his 45,000 Twitter followers (@BrekShea) with the caption "locker room banter gone wild".
The incident triggered a series of angry messages from Jones's girlfriend Kissa Abdullah, who pointed out the religious sensitivities involved.
"It just takes a minute to be sensitive to someone's beliefs no one says u can't have a sense of humour but let it be a joke! This wasn't!," she said on Twitter.
- Sports & Recreation