Carter, a 16-year veteran who had never before been suspended, will sit out Friday night's road game against the Minnesota Timberwolves.
Carter was assessed a flagrant 2 foul and ejected from Wednesday's game in the third quarter for intentionally striking rookie center Steven Adams in the head with his right forearm and elbow. It was retaliation for Adams elbowing Carter in the face while protecting the ball seconds earlier.
Carter publicly apologized to fans for the incident after the game.
"More than anything, there's a lot of people watching the game of basketball and they want to clean that stuff up because it's not needed," Carter said. "You hate to see it. That's why I wanted to apologize to all fans and all the people watching.
"It was just a reaction. It was just one of those things where you get caught in the moment playing in a big game, in a battle. It does happen, but sometimes when you do something like that, you just wish you can take it back."