The Tigers made the announcement on their official Twitter account, saying that Cabrera had "successful core muscle repair surgery."
Cabrera told ESPNdeportes.com's Enrique Rojas that the surgery "repaired three muscles in my groin that connect to my abdomen."
The operation was performed by Philadelphia-based surgeon William Meyers, who also examined Cabrera before the postseason.
Cabrera, who was visibly limited by the injury over the past two months, will undergo rehabilitation for the next six to eight weeks, the team said.
"The doctor said he didn't understand how I could have played with so much pain," Cabrera told Rojas. "It hurt so much that I almost couldn't lift my right leg, and that was the reason I couldn't reach the outside fastballs at the end of the season."
Cabrera, 30, batted .348 with 44 home runs and 137 RBIs this season en route to his third consecutive American League batting title.
But the All-Star third baseman hit just .262 with two homers in 11 postseason games. The Tigers lost to the Boston Red Sox in the AL Championship Series.
Cabrera recently told Rojas that he consulted with the Tigers before deciding to play through the injury.
Cabrera, who became baseball's first Triple Crown winner in 45 years last season, is considered a favorite to repeat as the AL MVP. The last AL player to win back-to-back MVP Awards was Chicago White Sox slugger Frank Thomas in 1993-94.
"I don't play to win trophies," Cabrera told Rojas. "But if I get the MVP, I hope to be recovered enough to lift it up."