The 24-year-old Arthur, who was picked in the first round of the 2008 NBA Draft coming out of Kansas, suffered the injury during a pickup game earlier in the week. Arthur could return earlier than the projected 4-6 weeks if he progresses well and is symptom free, the team said.
Arthur averaged 9.1 points and 4.2 rebounds in 2010-11 and was projected to be the top backup option for center Marc Gasol and forward Zach Randolph this year after the Grizzlies traded Dante Cunningham to the Minnesota Timberwolves in the offseason.
If Arthur can return in the expected timeframe, he should be available for the Grizzlies at the start of the regular season but would miss a significant amount of training camp.
Arthur was sidelined all of last season with a torn ACL.