Capps first felt the discomfort when he woke up on Saturday, and hasn't pitched since giving up a two-run homer in the ninth inning of Friday's 5-3 loss to the Brewers.
He threw a light bullpen before Tuesday's game against the Pirates, but isn't expected to return until Wednesday or Thursday. Right-hander Jared Burton and left-hander Glen Perkins are expected to serve as co-closers -- depending on matchups -- in Capps' absence.
"Cappy went out and threw in the bullpen a little bit, feels good enough, but we're not going to use him," Twins manager Ron Gardenhire said. "We're going to back him up another day at least, maybe two. We want him to be healthy, and he's not totally there yet."
Capps said he took some anti-inflammatory medication for his shoulder and that it's feeling better. He added he feels he could return, but is OK with Gardenhire and pitching coach Rick Anderson's decision.
"I just threw a touch and feel," Capps said. "It felt all right. I still have a little soreness in there. I certainly feel good enough to compete. That's Gardy's decision and Andy's decision and the trainer's. Whatever they want to do."