The St Mirren captain was offered the sanction by the Scottish Football Association's compliance officer, Vincent Lunny, for allegedly striking United's Stuart Armstrong in the face during the teams' match at St Mirren Park on Boxing Day and has accepted the punishment. The Irishman will now sit out the matches away to Kilmarnock on Thursday and at home to Celtic on Sunday.
The incident was missed by the referee Bobby Madden but later posted online by Dundee United on their Twitter and Facebook pages. Jackie McNamara, the United manager, was also critical of Goodwin during his media interviews following the match that St Mirren won 4-1. That has angered the Paisley club who condemned United' actions.
"As a club we were disappointed to find one of our players singled out for criticism by another football club both in the media and thereafter on their website," read a statement.
"We accept that football is a game of opinions but we find this unacceptable. As a club, we have on many occasions been aggrieved by decisions, tackles and challenges made on our players. We have, however, dealt with such matters behind closed doors, via the appropriate channels and in a professional manner. We are of the view that one club should not be commenting on another club's players in public and feel that these issues should be dealt with by the governing body [Scottish FA] to protect the integrity of the game."
Earlier, Lennon had also been critical of United's stance. "What has frustrated me is that a lot of good things happened in the United game that were overlooked. If United had won that game, we would all have been talking about their good young players and I thought our youngsters on the day were terrific. This incident with Jim has claimed the headlines instead and that disappoints me.
"What also disappoints me is the reaction of other clubs, putting things out there when already the SFA are well on top of things."
In September, Stephen Thompson, the Dundee United chairman, spoke out against the idea of clubs highlighting incidents involving other clubs' players.
"It's not the clubs' job to start highlighting incidents of player discipline from other clubs; that's what we have match officials and supervisors for," he said. "That's really wrong. It opens a can of worms.
"What happens if we're playing club X next week and we see something on TV from their game at the weekend that hasn't been highlighted? We report it and that gets the player banned? That's totally and utterly wrong. It's up to the authorities to handle these things properly."