Perez was hurt during a bullpen session on Thursday in his first workout at spring training. The Indians are hopeful that he will begin throwing again toward the end of spring training and will be ready for the start of the season on April 5.
"Thanks for all of the support; just a little set back," Perez wrote Sunday on Twitter. "At least it's not the moneymaker. I'll be ready for opening day."
The 26-year-old right-hander was an All-Star for the first time in 2011 and finished the season with 36 saves in 40 chances. He posted a record of 4-7 with a 3.32 earned run average.
Perez, acquired from St. Louis just before the 2009 trade deadline, has 59 saves in 67 opportunities over the past two seasons.