Barton was banned and fined £75,000 on Wednesday by a Football Association-appointed independent regulatory commission after he elbowed Carlos Tevez in the face and then kicked out at Sergio Aguero as he left the pitch.
QPR are now carrying out their own investigation into the incident.
The club said in a statement: "Queens Park Rangers Football Club can confirm it has now started a full internal investigation in relation to Joey Barton's dismissal and subsequent events against Manchester City on the final day of the 2012/13 Barclays Premier League season.
"The QPR midfielder will not appeal against the independent regulatory commission's decision made on Wednesday and he and his team are now working in full cooperation with the club to assist in the internal investigation.
"The club expects the investigation to last at least two weeks.
"During this period, no one from the club or Joey Barton himself will make any further comment."