Bourn had the operation Tuesday in Dallas. The team said Bourn will need six weeks to recover at his home in Houston before he can begin his normal offseason program.
The 30-year-old leadoff hitter sustained the injury while trying to steal second in the ninth inning of the Indians' game Sept. 29 at Minnesota. Cleveland clinched an AL wild-card playoff spot with a 5-1 win.
Bourn played three days later in the wild-card game against Tampa Bay, but he went 0-for-4 and struck out twice. Cleveland lost 4-0.
He batted .263 with six homers and 50 RBIs in his first season with the Indians, who signed him to a four-year, $48 million contract in February.