Manager Kevin Cash announced the news before the game in Minnesota on Friday night.
Kittredge, 32, went on the injured list Thursday, but the initial expectation for treatment was a minor procedure to remove loose bodies in the elbow. After further examination, he will need the ligament replacement and likely more than a year to recover.
Kittredge had just returned Sunday from a 17-game absence due to lower back tightness. Then after his second appearance since being reinstated from the injured list, he felt his arm lock up and couldn't straighten it. Kittredge has five saves in eight attempts and a 3.15 ERA in 17 games.
The Rays have 11 pitchers on the injured list, including six relievers. Kittredge joins Nick Anderson, J.T. Chargois, Pete Fairbanks and J.P. Feyereisen as key late-inning options who are currently on the shelf. Anderson and Fairbanks have yet to pitch this season.
The Rays also placed their other 2021 All-Star, catcher Mike Zunino, on the injured list Friday with inflammation in his left shoulder. He'd been playing through soreness for several weeks.
"It got to the point where it's affecting everything a little bit, even catching, so definitely swinging," Cash said. "Feel like we want to calm it down, and hopefully it's a shorter stint."
Zunino hit a career-high 33 home runs with an .860 OPS in 109 games last year. He's batting just .148 this season with five homers and a .499 OPS in 36 games.