The team announced the injury Friday night. Marte was leading the NL with 187 hits when he was shut down, batting .329 with 32 homers and 92 RBIs.
Marte, 25, was out of the lineup Wednesday at home against Miami. He had a precautionary MRI after leaving Tuesday's game in the fifth inning with back stiffness.
"You can't measure my level of disappointment because he was such an important player to this team, this organization," manager Torey Lovullo said. "That's obvious. But what I'll focus on is what he meant to this team, the development that he showed over the course of this year. That's all I can look at right now.
"He was a special player, he was a special man, and it's a special story. We're going to remember the year he had because of what he went out there and accomplished."