The move was made retroactive to Aug. 5.
Perez, 27, left Friday's game against the Seattle Mariners after six innings, and an MRI revealed the injury.
"All of our core guys are really pretty indispensable,'' manager Ned Yost said.
He said the "worst-case scenario was four weeks'' for Perez being out, but he was hopeful it would be in the 10-to-14 days range. Yost said the club is expected to know more Monday about the extent of Perez's injury when the swelling diminishes.
Drew Butera, who entered Sunday hitting .250 with two home runs and nine RBIs in 92 at-bats, will do the majority of the catching in Perez's absence.
Perez is hitting .278 with 21 home runs and 65 RBIs this season for the Royals, who enter Sunday's game three games behind the first-place Cleveland Indians in the AL Central. The Royals hold a one-game lead over the Tampa Bay Rays for the second wild-card spot.
Catcher Cam Gallagher was recalled from Triple-A Omaha to fill the roster spot. Gallagher, 24, is hitting .294 with five home runs and 34 RBIs this season, and will be making his major league debut.
This is Perez's first trip to the disabled list since 2012 when he had a knee injury. He also was placed on the 7-day bereavement list in 2013. He missed six games last season with a quad contusion.
"We've been through this before,'' Yost said. "This is nothing new to us. You just deal with it and move on. Guys understand. We'll have Drew and Cam here to pick up the slack behind the plate. We feel like we can cover it.''
The Associated Press contributed to this report.