The 28-year-old apologised to the Rovers’ midfielder for the incident in his side's 2-1 loss to Blackburn on Wednesday which, although missed by referee Michael Jones during the match, led the Football Association to take retrospective action.
"I fully accept that I was in the wrong on this occasion and accept the charge that the FA have brought against me,” Barton told Newcastle’s official website.
"I would like to apologise to Chris Hughton, my team-mates, our supporters and of course to Morten Gamst Pedersen and Blackburn Rovers.
"This season, I have really been enjoying my football and although I have been on the receiving end of a few robust challenges, I have, up until now, remained calm in the face of provocation and just carried on with the game.
"But I hold my hands up, I reacted badly to the situation on Wednesday night and I deeply regret it.
"I have been working very hard to keep that side of my game under control and I think it has showed in the way I have been able to get on and enjoy my football this season.
"I look forward to trying to get back into the team once my suspension is over and helping the club maintain its good start to the season."
Newcastle manager Chris Hughton added: "We accept the action taken by the FA, and it is of course disappointing to lose Joey for three games. He has worked so hard on his game this season, but he knows that he can't react the way he did on Wednesday."
Barton will now miss his club’s games against Fulham, Bolton Wanderers and Chelsea.