Club officials said Greinke had gone back to his home in Orlando, Fla. The 22-year-old right-hander, a first-round draft pick in 2002, was 5-17 with a 5.80 ERA in 33 starts last season.
"He's gone home for personal matters," Royals manager Buddy Bell said. "That's all I can say about it. He's just got permission to go home and take care of a few things. I hate to be so vague, but hopefully this will be taken care of sooner, if not later."
General manager Allard Baird said he does not know when Greinke will be back.
"There is no timetable," Baird said. "We'll support him and we go from there."
He appeared in 35 minor-league games before making his major-league debut on May 22, 2004, at the age of 20 -- the third-youngest starter in club history.