Kelley hasn't pitched since May 6 and was not available on Monday, when the Yanks' bullpen frittered away a late lead by allowing five unanswered runs in the final three innings to the Mets.
"It's just not getting to where it needs to get, and now we're looking at seven days, eight days," manager Joe Girardi said. "So we figured with the health of our outfielders, the way they are, it's probably a good idea to call up Zoilo and go from there."
Kelley is 1-2 with a 3.52 ERA and four saves in 16 games this season. Kelley said that he first started to be bothered by the stiffness during the Yankees' series against the Angels in Anaheim last week.
"It's just a waiting game at this point," Kelley said after the Yanks' 12-7 loss to the Mets on Tuesday. "It could start to feel better any day. The what-if game and continuing to be a man short, we can't keep doing that."
"It's a blow to our bullpen. Any time you lose anyone in your bullpen, it's a blow," Girardi said. "When you start talking late-inning guys, it puts a little more responsibility on [Adam] Warren and [Dellin] Betances. Those guys will have to step up. They've been stepping up all year for us."
Signed as an amateur free agent in 2005, Almonte was batting .273 with six homers and 24 RBIs in 33 games at Triple-A. The 24-year-old made his big league debut last season, posting a .236 average with one homer and nine RBIs.
Girardi said that with Kelley deleted from the bullpen mix, he would likely use Warren in the eighth inning and Betances in the seventh. Girardi would also entertain calling upon closer David Robertson for more than three outs.
"I might have to. I was going to do it last night; we didn't get to that spot, but it might be a situation he has to do it tonight," Girardi said.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.