The procedure will be performed by Dr. Riley Williams III at the Hospital for Special Surgery in New York, N.Y. Wright is expected to be ready by the start of the 2018 season.
Wright, 32, was 1-3 with an 8.25 ERA through his first five starts this season before being placed on the disabled list with a sprained left knee.
Red Sox president of baseball operations Dave Dombrowski said the right-hander injured the knee during spring training, but it wasn't bad enough for him to start the season on the DL.
Wright, 32, was a first-time All-Star in 2016, going 13-6 with a 3.33 ERA in 24 starts. However, he also missed significant time after suffering bursitis in his right shoulder while sliding back to second base as a pinch runner during an interleague game in August.