A candidate to become Detroit's eighth-inning setup man, Rondon felt discomfort Monday after pitching a scoreless inning against Washington the previous day.
Detroit general manager Dave Dombrowski said Rondon was examined Wednesday by Dr. James Andrews, and an MRI revealed the tear. Dombrowski said the 23-year-old will have surgery next week.
''He just came in one day and said he was a little tender,'' Dombrowski said Friday. ''At that point, we figured he should see a doctor. Before that, he hadn't complained of any problems at all.''
Rondon becomes the latest pitcher hurt during spring training and headed to Tommy John surgery, following Atlanta's Kris Medlen and Brandon Beachy, and Oakland's Jarrod Parker. Arizona's Patrick Corbin also may need the procedure.
Rondon was 1-2 with a 3.45 ERA as a rookie last year, striking out 30 in 28 2-3 innings, and he had a 1.29 ERA in seven spring training games this year.
Dombrowski said the Tigers, who signed Joba Chamberlain during the offseason, will fill Rondon's spot internally.
''We feel we have a lot of depth there,'' Dombrowski said. ''Some guys will have to step up and I think they will.''
Rondon was competing with Chamberlain for the eighth-inning role leading to closer Joe Nathan. Now Al Alburquerque will likely get some of those opportunities, and expanded roles may go to Evan Reed and left-handers Ian Krol and Phil Coke.
The Tigers have been beset by injuries. Shortstop Jose Iglesias could miss the entire season because of stress fractures in both legs; Andy Dirks, slated to platoon in left field, will miss the first two months after back surgery.
Asked how he was holding up, first-year manager Brad Ausmus joked, ''I just bought my first pack of Marlboros'' - a reference to former manager Jim Leyland's smoking habit.