The SEC ruled Friday that the matter would be handled internally by the two schools.
Dial's above-the-shoulder, helmet-to-helmet hit on Murray took place away from the play on an interception return, leaving the junior quarterback hurt on the turf, though no flag was thrown on the play.
"The Southeastern Conference has completed its review of video from the 2012 SEC Football Championship Game. Several plays involving both teams were reviewed," the SEC said in a statement.
"After review, all subsequent action will be handled internally by the two institutions and the conference office is satisfied with their actions."
Dial, a junior college transfer and one of nine scholarship seniors on the team, has started on the Alabama defensive line for most of the season, racking up 21 tackles, one sack and 4.5 tackles for loss.
The SEC also opted against punishing Georgia cornerback Sheldon Dawson, who had been accused of trying to eye gouge Alabama's Dee Milliner while players from both teams attempted to recover a fumbled kickoff early in the fourth quarter.
Georgia coach Mark Richt said Dawson has been disciplined internally and will not face game punishment in the Bulldogs' Jan. 1 matchup with Nebraska in the Capital One Bowl.
"To me it looked very bad," Richt said after Friday's practice. "It's just not Georgia football. I think when he saw it, he said, 'Coach, I saw it and I don't blame you.' He didn't even make an excuse. He just said, 'When I saw it, it looked bad and I'm sorry.' "
Although he admitted it looked blatant, Dawson said the eye gouge was unintentional and that he apologized to Milliner almost immediately.
"I don't think I even touched him in the eye -- but it does look like I got him in the eyes," Dawson said. "But I apologized to him and I apologized to a couple people that I know that know him and stuff, too. It wasn't the way it seemed, but it should have never happened."