City confirmed on their Web site (www.mcfc.co.uk) that a player had been suspended but did not reveal his identity.
"We can confirm that a player has been suspended until the end of the season, pending an internal investigation into a training incident at the Carrington complex," the Premier League club said in a statement.
"The club will be making no further comment at this time."
The BBC reported that Barton and French midfielder Ousmane Dabo were involved in a fight at training and that Dabo had gone to hospital with mouth injuries.
Barton's agent Willie McKay, who has not yet spoken directly to the England midfielder, played down the incident.
"As far as I've heard, he was defending himself. But because it is Joey it makes headlines," he told the BBC.
City are due to host Premier League leaders Manchester United at Eastlands on Saturday.
