The Frenchman will miss one game and he will be eligible to participate in a second play-in game, if necessary.
Gobert left Sunday's game after the altercation that came during a time out in the first half of the team's 113-108 victory over the New Orleans Pelicans.
Anderson repeatedly hurled insults at Gobert on a night when the veteran three-time All-Star was playing hurt, ESPN reported.
"Emotions got the best of me today," Gobert tweeted Sunday night.
"I should not have reacted the way I did regardless of what was said. I wanna apologize to the fans, the organization and particularly to Kyle, who is someone that I truly love and respect as a team mate."
The Timberwolves are seeded eighth in the Western Conference and will play the seventh-seeded Los Angeles Lakers on Tuesday for a chance to face the second seeded Memphis Grizzlies in the first round of the playoffs.
If the Timberwolves lose to the Lakers, they will play the winner of the Pelicans-Oklahoma City Thunder play-in game, with the winner to take on the top-seeded Denver Nuggets in the first round.
The 30-year-old Gobert has been named Defensive Player of the Year three times. He averaged 13.4 points, 11.6 rebounds and 1.2 assists in 70 games for the Timberwolves this season.
