New York announced the decision Wednesday night during the second game of a doubleheader against the Baltimore Orioles.
Andújar, last year's AL Rookie of the Year runner-up, initially was sidelined by the injury from April 1 to May 3 and struggled mightily in his return.
After going 6 for 47 with no extra-base hits, he went back on the injured list Monday. Manager Aaron Boone had said Andújar was discussing a possible operation with the team and his family.
"Hurt for him a little bit," Boone said. "But know this is also just the beginning of the road back."
Yankees head team physician Christopher Ahmad will perform the surgery Monday at New York Presbyterian Hospital.
The 24-year-old Andújar was a major factor in the Yankees' run to a playoff spot last season, hitting .297 with 27 home runs and 92 RBIs.
"Miggy's beloved in that room and obviously really important to us between the lines and just who he is," Boone said. "Hopefully this is a really good step for him and starting the healing process."
Minus Andujar this season, the Yankees have relied on Gio Urshela at third base. Newly acquired slugger Kendrys Morales is likely to pick up the bulk of the DH duties until some of New York's other injured hitters return.