Martin had surgery in September on his left foot to repair a fracture. He was scheduled to have a follow-up procedure in the offseason, but his discomfort forced the Grizzlies to address the issue immediately.
Before Friday night's Game 3 against the San Antonio Spurs, Memphis coach Dave Joerger said that Martin is devastated by this latest injury.
"My heart breaks for him," Joerger said. "He's going to be out for quite a while it sounds like. It's a tough deal, you know. He's one of the kindest, most soft-spoken, quietest, nice guys we have on the team."
Martin joins a lengthy list of injured Grizzlies. Memphis is also missing Mike Conley (left Achilles tendinitis), Marc Gasol (right foot fracture), Jordan Adams (right knee surgery) and Brandan Wright (right medial collateral ligament sprain).
The Grizzlies said forward JaMychal Green is probable for Friday night's game with flu-like symptoms.
The 6-foot-10 Martin was Memphis' first-round draft pick last June with the 25th pick overall, out of LSU. He didn't make his NBA debut until Dec. 18 after needing the offseason surgery on his left foot. He played in 27 games and averaged 5.7 points and 3.2 rebounds as a rookie.
He scored five points in Game 1 and four in Game 2. San Antonio leads the best-of-seven series 2-0.
The Associated Press contributed to this report.