The Knicks are hopeful Anthony will not need surgery, according to the source, who added the team plans to allow its All-Star to rest for the next three-to-four weeks in an attempt to allow the injury to heal.
If it is not healed at that point, then surgery will be considered, the source said.
Dr. Neil Roth, an orthopedic surgeon at New York's Lenox Hill Hospital who specializes in sports medicine, estimates surgery could sideline Anthony for four months. Roth has not treated the Knicks' forward.
The New York Daily News earlier reported Anthony's injury.
Anthony said Monday that the injury, suffered on April 14 against the Indiana Pacers, hampered him throughout the postseason.
The Pacers were also physical with Anthony in the next round, and he appeared to tweak the injury throughout that series.
Anthony shot 40.9 percent from the floor in 12 postseason games after shooting 45 percent during the regular season.
Anthony never complained about the injury, nor did he use it as an excuse during the postseason. However, it was clear he was in pain.
"To be able to play with that and get through the pain, it just came a point where you just try not to think about it," Anthony said Monday. "That's where I was at mentally."