The forward played New York's 12 playoff games with the injury, which it appears will not require surgery, according to Marc Berman of the New York Post.
The Knicks have reportedly told Anthony to rest for the next 3-4 weeks with the hope that the tear will heal on its own. At that point, he will be re-evaluated.
Had surgery been necessary, Anthony would have sat out 3-5 months, jeopardizing his status for the start of training camp.
Anthony originally hurt his arm on April 14 in a game against the Pacers and had been feeling chronic pain ever since. He appeared to have re-aggravated the injury in Game 5 of the Knicks' first-round playoff series with the Celtics.
Still, he averaged 29.2 points per game for the Knicks throughout the playoffs, leading them to their first postseason series win in over a decade.