Parnell, who turns 29 on Sunday, was placed on the disabled list July 31. He emerged as a solid closer this season, with Frank Francisco missing most of the year with right elbow discomfort.
Parnell was 5-5 with a 2.16 ERA and had 22 saves in 26 chances before becoming sidelined.
He remains under the Mets' control through the 2015 season. He earned $1.7 million this season and again is eligible for arbitration this winter.
Parnell had tried to avoid the procedure. He first rested for several weeks and received an epidural injection to try to get the issue resolved without surgery.
General manager Sandy Alderson said Parnell should be ready for the start of spring training.
Parnell was due to have the surgery performed by Dr. Robert Watkins in California.
"We expect him to be," Alderson said about Parnell's readiness for 2014.