The Grizzlies announced Melton's injury Thursday in a team release. Grizzlies officials said Melton should return to basketball activities in four to eight weeks.
Melton, who is 6-foot-4, played 50 games for the Phoenix Suns last season and averaged 5 points, 3.2 assists, 2.7 rebounds and 19.7 minutes.
The Grizzlies acquired the 21-year-old Melton along with forward Josh Jackson and two future second-round draft picks over the summer in a trade that sent forward Kyle Korver and guard Jevon Carter to Phoenix.
The Suns later waived Korver, who ended up signing with the Milwaukee Bucks.