The Knicks star was sanctioned after engaging in verbal confrontations with Garnett both during and after the Celtics' 102-96 win over New York Monday.
Anthony screamed at Garnett as both teams were heading to their Madison Square Garden locker rooms following game, and television footage later showed him waiting outside the Celtics' team bus, apparently in an effort to confront Garnett.
Several police officers and team officials surrounded the superstar center, preventing him from moving toward the bus.
"There are no circumstances in which it is acceptable for a player to confront an opponent after a game," NBA Executive Vice President Basketball Operations Stu Jackson said. "Carmelo Anthony attempted to engage with Kevin Garnett multiple times after Monday's game and therefore a suspension was warranted."
Anthony told reporters Tuesday he just wanted to "talk to KG" and didn't do anything to be suspended, adding he was angered by "trash talk" of a personal nature allegedly hurled at him by Garnett during the contest.
Anthony, the Knicks' scoring leader at 29 points per game, will sit out Thursday's contest at Indiana.