After viewing a recording of the match, SFA compliance officer Vincent Lunny deemed the Irishman to have violated Rule 200 by striking opponent Stuart Armstrong in the face, an incident which went unpunished by referee Bobby Madden.
A two-match fixed suspension has been offered to Goodwin, who was substituted by manager Danny Lennon later in the first half after picking up a yellow card for a challenge on United midfielder John Rankin.
He has until 3pm on Tuesday to respond to the charge and should he choose to have the matter heard by a tribunal a provisional date of Friday, January 3 has been set.
After the match on Boxing Day, a furious Dundee United boss Jackie McNamara was adamant Goodwin should have seen red for his clash with Armstrong.
In his post-match interview, McNamara said: "I was disappointed with some of the challenges that went in.
"That was reflected in the substitutions that Danny made before the end of the half. Jim could have been sent off before that.
"It wasn't just the number of fouls but the manner in which some of them were carried out."