The 40-year-old Kent can begin rehabilitation soon after the operation and might return by the end of the season, manager Joe Torre said.
"We'll see what happens," Torre said. "I know one thing: If there's a chance he'll come back, he's going to come back."
Dodgers general manager Ned Colletti said the club will place Kent on the 15-day disabled list and recall infielder Chin-lung Hu from Triple-A Las Vegas.
Kent is batting .275 with 11 homers and 57 RBIs.