New York announced the decision Wednesday night during the second game of a doubleheader against the Baltimore Orioles that the Yankees swept.
Andujar, last year's American League Rookie of the Year runner-up, initially was sidelined by the injury from April 1 to May 3, and he struggled mightily in his return.
After going 3-for-34 with no extra-base hits, he went back onto the injured list on Monday. Manager Aaron Boone had said Andujar was discussing the possibility of an 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 is expected to perform the surgery on Monday at New York Presbyterian Hospital.
The 24-year-old Andujar 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."
Without 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 designated hitter duties until some of New York's other injured hitters return.
The Associated Press contributed to this report.