Hours before Wednesday night's regular-season opener against Indiana, the Pelicans said team doctors discovered the injury after Anderson experienced discomfort during recent practices.
Anderson said the injury began to bother him on Monday.
"I honestly don't know exactly what it was that did it, but after practice I felt it and it was pretty painful," Anderson said. "I went in to get an X-ray and the X-ray looked good, but I guess they had to do a double take on it and they found a small little chip."
The 6-foot-10 Anderson is one of New Orleans' top 3-point shooters. Last season, he averaged a career-high 16.2 points per game and shot 38 percent from 3-point range. He also grabbed 6.4 rebounds per game.
When available, Anderson is expected to be one of New Orleans' top players coming off the bench and play significant minutes.
Anderson, who is able to walk normally, said the injury will not require surgery.
"It's kind of just a pain-tolerance level," Anderson said. "I'm going to keep working on it and I'm going to get back as soon as I can, as soon as it feels good."
Coach Monty Williams did not single out any players for more time on the court in Anderson's absence, saying it would be a full team effort.