Wright hasn't played since mid-April. He originally went on the disabled list with hamstring trouble, then developed a back issue.
The Mets said Saturday that the seven-time All-Star has been diagnosed with stenosis, a narrowing of the spinal column. The team captain took live batting practice on Friday before his back flared up again.
Wright will rest for at least a week before being reassessed.
"It's just something that seems to be taking longer than we initially thought," Mets assistant general manager John Ricco said. "The way it was progressing, (doctors) thought it would be gone by now."