Martin injured his left quad in the team's regular-season opener and has not played since. He had also been bothered by a left knee injury in the preseason and it had recently begun giving him problems.
Martin signed a four-year, $31.3 million contract this past offseason to remain with the Hornets.
The team said Martin will be reevaluated in four weeks.
Martin, now in his fourth NBA season, is considered Charlotte's best defensive player. Martin averaged 7.7 points and four rebounds per game last season. He was generally considered Charlotte's sixth man, playing in 52 games with 10 starts last season.
The Hornets, who have lost seven straight games, play at Miami on Saturday night.