No surgery is required.
Anthony will sit out the final two games of the season and will be re-evaluated in a month, the team said.
Anthony had been playing through pain in his right shoulder since aggravating the injury on April 2 against the Nets.
Coach Mike Woodson said an MRI taken earlier Tuesday revealed the tear. Woodson anticipates that Anthony will be able to resume basketball activity in a month.
"Obviously, he knew it was bothering him when he hurt it two weeks ago but he hung in with us trying to make this last push to get in the playoffs," Woodson said.
Anthony played in four games after initially hurting the shoulder, including a game Sunday against the Chicago Bulls after the Knicks were eliminated from playoff contention.
Anthony took a significant risk playing with the injury because he plans to test free agency this summer.
Anthony said recently that there was "no way" he would sit out games while the Knicks were in playoff contention.
Now that he is officially out for the final two games of the regular season, there is a chance that Sunday's game against Chicago was Anthony's final game with the Knicks.
The 30-year-old Anthony should have a number of suitors on the open market. The Knicks can sign him to a five-year contract worth $129,135,806. If he signs with another team, the maximum he can get is $95,897,372 over four years.
Anthony is coming off one of his best seasons as a professional.
Entering play Tuesday, the All-Star forward was ranked second in the NBA in scoring (27.4 points per game). He finished the season averaging a career-high 8.1 rebounds per game. But he will miss the postseason for the first time in his 11-year career.
"I feel for him more than anybody," Woodson said. "The kind of season that he had, he deserves to be in the playoffs. I feel bad about that."
Anthony is no stranger to shoulder injuries.
He suffered a torn rotator cuff and partially torn labrum in his left shoulder late last season and played through the injuries in the playoffs.
Anthony eschewed surgery last summer and spent most of the offseason last year rehabilitating the injury. The shoulder remained healthy throughout the season.