It's the first career trip to the disabled list for the 27-year-old Perez. He was scheduled to be examined and have an MRI in Cleveland on Monday.
Manager Terry Francona said right-hander Vinnie Pestano (1-1, 5.25 ERA) would close games for the Indians during Perez's absence.
Left-hander Nick Hagadone was recalled from Triple-A Columbus and is in Cincinnati for the Indians' game against the Cincinnati Reds on Monday afternoon and gave up the winning home run. Going into the game, Hagadone had a 7.20 ERA in 10 innings over 13 combined appearances in his first two stints with the Indians this season.
The right-handed Perez felt stiff while warming up Sunday and was forced out of Sunday's game against the Boston Red Sox with two outs and a 2-1 count on Jacoby Ellsbury. The Boston star followed with a two-run double on Joe Smith's first pitch, capping a four-run, ninth-inning rally that lifted the Red Sox to a 6-5 win.
Perez said after Sunday's game that he had "been dealing with a little thing for the last couple of weeks, but we stayed on top of it and it had been getting better. But [Sunday] it took a couple steps back."
"I don't want to leave that mound at all, especially with the game on the line like that and the team trying to cling to a win," Perez said Sunday. "But you can't pick when you're going to get hurt and unfortunately right now it's a little sore."
Walks to Jonny Gomes and Jose Iglesias around Stephen Drew's single loaded the bases. On his third pitch to Ellsbury, Perez felt a pinch in the shoulder. With Francona watching at his side, Perez threw a warm-up pitch that sailed past catcher Carlos Santana.
"It kind of pinched on me and sent a little pain down my arm," Perez said Sunday. "Then I tried to throw another pitch and it just wasn't happening."
Perez is 2-1 with six saves and a 4.32 ERA for the Indians (27-22, second place in the AL Central). He has two blown saves. He has saved more than 30 games each of the past two seasons, including a career-best 39 in 2012.
Information from The Associated Press was used in this report.