He is expected to miss 10-12 weeks and the Royals will move Mark Teahan to third.
Gordon, who was the second overall pick in 2005, was struggling early in the season (2-for-21 in seven games).
"Gordon is a big part of the team," Teahen said. "But we're off to a good start and we have a deeper team this year.
"It's not a huge adjustment for me. I've been able to go back and forth from the right field to third before."