Teixeira told reporters he will follow doctors' advice to repair the wrist, which he first injured in spring training.
After playing in just 15 games this season, the slugging infielder was put back on the disabled list June 18 as the wrist continued to give him trouble despite receiving a cortisone shot.
A magnetic resonance imaging exam revealed a tendon sheath in the wrist has not healed properly.
Teixeira said the procedure requires four to five months of rest and rehabilitation.
After supplying 135 homers and 425 RBI in his first four seasons with New York, he has managed just a .151 batting average with three home runs and 12 RBI in 53 at-bats this season.