Green had an exam Monday that included X-rays and an MRI, confirming the injury. He was injured early in the second quarter of the Spurs' 104-86 win Sunday against the Minnesota Timberwolves.
Making his second consecutive start after coming off the bench in 11 straight games, Green missed his only field goal attempt and had three rebounds in nine minutes before his injury. He is averaging 7.4 points, 3.0 rebounds, 1.3 assists and 1.1 steals in 39 games.
Green, 26, is the latest key player to be injured for the Western Conference-leading Spurs (29-8), joining center Tiago Splitter, out since Jan. 5 with a sprained right shoulder, and shooting guard Manu Ginobili, who has missed the past two games with a hamstring injury.
The Spurs visit New Orleans to play the Pelicans on Monday night.
The Associated Press contributed to this report.