The closing role will be handled by a "committee" until Soria returns, he said.
Both Hillman and Soria insisted earlier this week that he was fine despite not appearing in a game for eight straight days. He returned on Wednesday night to post a save at Cleveland but apparently felt stiffness on Thursday.
Soria was confident that it was "nothing serious" and that he'd be back soon.
"I'll be all right, I'll be OK," Soria said. "It just feels stiff, not too bad."
Hillman said he'd kept Soria's situation under wraps until now to avoid tipping off opposing teams.
General manager Dayton Moore said the stiffness came to the Royals' attention last Saturday at Texas while Soria was warming up as a potential replacement for Zack Greinke, who finished his nine-inning shutout.
"He felt some tightness Saturday warming up for Greinke. That's why he wasn't in there Sunday," Moore said. "Then he felt really good in the Cleveland series, and he felt really good the night he pitched ... he just came in the next day [Thursday] and felt tight."
In Sunday's eighth inning at Texas, the Royals led, 5-3, and Ron Mahay and Jamey Wright gave up the tying runs. With the score tied at 5, Kyle Farnsworth was brought in for the ninth and gave up a game-ending home run to Michael Young.
Soria confirmed that scenario, but there was no indication from Hillman that anything was amiss.
"I've always been of the belief that the more information you put out there, the more it weakens your position -- especially when it's your closer," Hillman said.
Moore had no problem with that.
"You'll manage differently perhaps," Moore said. "[Tigers manager] Jim Leyland will manage differently if he knows Joakim Soria is not down there."
Hillman said there was no pressing reason to put Soria on the 15-day disabled list now.
"You take a guy that is projected for three to five [days], and it could be longer, but even if it's a week to 10 days, you've still got the possibility of three, maybe four save jobs that could make the difference for you," Hillman said.
Might the Royals put Soria on the DL?
"It's just day-to-day now," Moore said. "If it continues, we might have to. If this was late in the season, depending on where we were [in the standings], he could probably pitch in a day or two, but we're just going to be cautious."
Soria missed 17 days of Royals Spring Training to be with the Mexico team in the World Baseball Classic. During his absence he pitched just two innings in games. So he missed a good deal of Cactus League work.
"He didn't get a lot of work in Spring Training, and there are just a lot of things he's trying to play catchup on a little bit," Moore said. "Joakim has always been real good about communicating how he feels, and if he can't go, he'll tell us. If he says he can go, we trust him."
Although he's not on the disabled list, Soria becomes the Royals' third high-profile player to be shut down. Right fielder Jose Guillen has been on the disabled list for 15 days with a hip injury and is expected to return on Saturday. Third baseman Alex Gordon underwent hip surgery a week ago and is not expected back before late June.
In addition, two relief pitchers are disabled -- John Bale since Spring Training and Doug Waechter since last Tuesday.