Details are sketchy so far but it is believed that the trouble was sparked by a family of Everton fans staying in the same hotel.
They were in the bar area, along with some City players, and appear to have made some comments which upset Barton.
The 22-year-old midfielder is alleged to have slapped a 15-year-old Everton fan and then became embroiled in a tussle with Dunne, who is said to have been acting as peacemaker.
“Midfielder Joey Barton is at the centre of the investigation,” reads a statement from Pearce on the City website.
“The players were given some time off after a squad meal last night. Richard Dunne was present but his behaviour was exemplary.”
The scuffle between Barton and Dunne occurred at around 2am local time, although it is thought that it took 3 hours to calm down the situation. The City squad then had a training session at 10am.