The right-hander underwent an arthroscopic procedure in New York to repair a tear in the labrum of his right shoulder and is expected to be out about a year.
"I heard it went well," Girardi said. "It was done today by Dr. [David] Altchek and Dr. [Christopher] Ahmad. The rehab doesn't start right now, but it starts now, basically. We're anxious to get this guy back, and now he's on the road to recovery."
Altchek, the Mets' team physician and one of the nation's leading arm specialists, was expected to perform the procedure alongside Ahmad, the Yankees' team physician.
Pineda, who came over from the Mariners this past offseason in a high-profile deal for top prospect Jesus Montero and right-handed pitcher Hector Noesi, began experiencing weakness in his right shoulder during an extended spring game, weeks after he felt discomfort during a regular Spring Training start.
Pineda was 9-10 with a 3.74 ERA in 171 innings last year as a rookie with the Mariners.