The injury takes Hochevar, who had a successful first season in the bullpen last year, out of the running for the Royals' final rotation spot. That likely narrows the field to right-handers Yordano Ventura and Wade Davis and left-hander Danny Duffy.
Hochevar was making his first Cactus League appearance on Monday.
"Hoch, after his second-to-last pitch against the White Sox [on Monday], felt a twinge in his elbow," manager Ned Yost said on Wednesday. "He ended up throwing a cutter to strike the guy out and felt OK coming in. Next day, it was real stiff and sore, so we went and MRId him yesterday and he's got a sprain of his ligament. So we're going to shut him down for a couple of weeks -- probably three -- and see where we're at."
When Hochevar does return, he would be on track to return to the bullpen, according to Yost.
"I think best-case scenario [is] if we could have him back by the end of May or the first of June, we'd be in good shape," Yost said. "After the shutdown and getting back on a throwing program, that's probably the best-case scenario."
Although Yost didn't say so, the worst-case scenario would be for Hochevar to have a reconstructive procedure on his UCL: Tommy John surgery. That usually puts pitchers on the shelf for a year or more.
"It's the ligament that they Tommy John all the time," Yost remarked.
Hochevar also has a muscle strain in the area, but the sprained ligament is the primary concern.
The MRI report, though, gave the Royals a measure of optimism.
"We were a little nervous that it could have been worse, so we think we got as good a report as we could've hoped for coming back," Yost said. "But again, you really won't know until three weeks [from now] where we're at."
However, the club announced that Hochevar would seek a second medical opinion from Dr. Neal ElAttrache on Thursday in Los Angeles.
Hochevar, 30, was being treated in the training room Wednesday and, through a team spokesman, deferred comment for the time being.
He was on a list of several candidates hoping for the fifth starting spot behind James Shields, Jason Vargas, Jeremy Guthrie and Bruce Chen. But after the first week of games, it's basically down to three pitchers.
"Realistically, you still have Ventura, Davis and Duffy fighting for that spot," Yost said. "Something has to happen for the other guys to really get into the serious mix. You probably need to lose one of those three guys or somebody has to go down, realistically."
Included in the long shots are Chris Dwyer and Everett Teaford, up from Triple-A Omaha. Rookie John Lamb and veteran Brad Penny are coming back from medical concerns. No. 1 prospect Kyle Zimmer is being held back because of an arm issue late last season.
"You never know. Go out and throw really well and we'll see where it is when you have to make a decision," Yost said. "I've been there on that side before, too, when guys come into camp and you don't even consider them, and all of a sudden, it's: 'Well, how can I not take him?' And there's a lot of guys that still have the opportunity to do that in there."
Hochevar was the first overall Draft pick in 2006 by the Royals after declining to sign with the Dodgers, who had selected him in both '02 and '05. Hochevar reached the Majors in September 2007.
For the next five years, Hochevar was a regular in the Royals' rotation. Of his 132 appearances, 128 were as a starter. His overall record was 38-59 with a 5.39 ERA.
In Spring Training last year, the decision was made to use Hochevar in the bullpen, and he did well. After being eased into the role, by the end of the season, he was used in a setup role for closer Greg Holland.
Over his 58 relief outings last year, Hochevar posted a 1.92 ERA with two saves, a 5-2 record and 82 strikeouts in 70 1/3 innings. He had two long scoreless stretches, the first 17 2/3 innings and later 12 2/3 innings. On Sept. 10 at Cleveland, he became the first Royals pitcher in history to face five batters and strike out all five.
Despite all that success in the bullpen, Hochevar wanted to give starting pitching another try. For now, that effort is on hold.