Greinke was not at Sunday morning's workout and the Royals said he had returned to his Orlando, Fla., home.
There was no indication when Greinke might return.
"I talked to him [Saturday]," manager Buddy Bell said. "He's gone home for personal matters. That's all I can say about it."
Bell declined to say if the matters were related to baseball or family or something else.
"It's none of my business, really," Bell said. "He's just got permission to go home and take care of a few things."
Sources said the Greinke departure was not the result of club discipline.
Greinke was scheduled to pitch a batting-practice session on Saturday, but did not, and the club said only that he wasn't feeling well.
He had met with Bell late last week, including a long session behind closed doors on Thursday.
"He's no different than he has been since I've been here," Bell said.
The other players were told about Greinke's departure during a preworkout meeting on Sunday.
Greinke, 22, is coming off a 5-17 season in which he made 33 starts. He led the American League in losses in his first full Major League season.
If Greinke is gone for an extended period, he could lose his expected spot in the rotation. He and Runelvys Hernandez were figured as starters along with newcomers Mark Redman and Scott Elarton.
"There's no question about the kind of talent he has," Bell said.
But the question remained about why Greinke had left.
"I hate to be so vague," Bell said, "but, hopefully, this will be taken care of, sooner if not later."
General manager Allard Baird shed no additional light on the matter.
"There's no timetable for his return," Baird said. "We'll support him, and we go from there."
Greinke's teammates seemed surprised.
"I didn't hear about it until this morning," said outfielder Emil Brown, a close friend. "I'm going to call him this afternoon. I hope he's OK."
"I don't know much about it," said fellow pitcher Jeremy Affeldt. "Maybe he just needs to take some time away, like some guys have done."
Greinke did not respond to phone messages.
Home run derby: The Royals lost a home run hitting contest to the Texas Rangers on Sunday, 14-8.
Alex Gordon cleared the fences four times for the Royals. That's four more than the Royals contingent hit in last year's contest, when they were shut out.
Lined up: Even before the first Cactus League game, Bell has his basic lineup in mind.
That would be David DeJesus leading off, followed by Mark Grudzielanek, Mike Sweeney and Reggie Sanders. The fifth-through-eighth holes will be filled by Doug Mientkiewicz, Emil Brown, Angel Berroa and Mark Teahen, the order determined in many cases by the opposing pitcher. Batting ninth: John Buck.
The set lineup gives Bell some measure of confidence.
"That's why I'm telling everybody we have a chance to turn things around," he said.
Intrasquad pitching: Denny Bautista and J.P. Howell will be the starting pitchers in Tuesday morning's intrasquad game at the Surprise complex.
Also scheduled to pitch: Mike MacDougal, Ambiorix Burgos, Adam Bernero, Jimmy Gobble, Bobby Keppel, Steve Stemle, Ryan Baerlocher, Juan Cedeno and Brian Bass.
There will be a short intrasquad game on March 1 with Scott Elarton, Mike Wood, Runelvys Hernandez and Joe Mays due to throw.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.