The 24-year-old leads the Major Leagues in steals with 30, including the final one, when the injury took place.
With Gordon out for at least six weeks after surgery Friday, the Dodgers will have to find new ways to put runners in motion on the bases.
"We aren't nearly as good in that regard without Dee," Dodgers manager Don Mattingly said. "It changes the leadoff spot and how we work around that. It does change things a little bit."
The Dodgers player with the next most stolen bases is Tony Gwynn Jr. with 10, followed by Elian Herrera and Mark Ellis with four.
"It takes a lot of our team speed away," Mattingly said. "I don't know if it changes everything we do, but it's something we'll have to deal with until he returns."