Team officials announced the decision Friday.
Martin played 27 regular-season games for the Grizzlies as a rookie last season and averaged 5.7 points, 3.2 rebounds and 14.1 minutes. The former first-round pick from LSU also played 10 games for the NBA Development League's Iowa Energy and averaged 15 points and 6 rebounds.
Martin didn't play Wednesday in the Grizzlies' season-opening victory over the Minnesota Timberwolves.
The Grizzlies selected the 6-foot-10 forward with the 25th overall pick in the 2015 draft.