New York made the announcements Tuesday, a day after Wright was examined by Dr. Robert Watkins in Los Angeles.
The 35-year-old Wright has been limited to 75 regular-season games during the past three years. He was on the disabled list from April 15 to Aug. 24, 2015, when he strained his right hamstring and then developed spinal stenosis.
He returned as the Mets won their first NL pennant since 2000 but has not played for them since May 27, 2016. Watkins operated that June 16 to repair a herniated disk in Wright's neck. After Wright's minor league rehabilitation assignment was ended after three games last year due to shoulder pain, he had surgery Sept. 5 to repair his right rotator cuff, and Watkins performed a laminotomy in early October in which a bony layer over the spinal canal was removed to treat nerve compression.
A seven-time All-Star, Wright is guaranteed $47 million by the Mets over the next three seasons. New York signed Todd Frazier in case Wright would not be able to play.
The 32-year-old Cespedes hurt his right wrist while swinging in a game on March 6. He was to play Tuesday but was scratched.
"I felt something in my wrist, but I didn't care much about that," Cespedes said through a translator. "It started bothering me on Tuesday, but with the day off yesterday ... I thought it would be good for today."
New York had X-rays taken and awaiting results.
Cespedes is starting the second season of a $110 million, four-year contract.
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