He is expected to be ready for spring training, the Mets added.
Hand specialist Andrew Weiland performed the procedure at the Hospital for Special Surgery in New York.
Duda, 26, hit .239 with 15 homers and 57 RBIs in 401 at-bats last season. He also spent a month in the minors during the summer.
The Mets need to resolve this offseason where Duda will play in 2013.
His natural position is first base, but he's blocked there unless Ike Davis is traded. Duda otherwise has shown more aptitude for left field than right field, although the Mets still have left fielder Jason Bay under contract for one more season.