Newsstand copies will be available closer to the weekend.
The 25-year-old right-hander is the first Royals player to appear on the cover since pitcher David Cone on April 5, 1993 for the magazine's baseball preview. The last Kansas City player to appear in an in-season cover was back on June 12, 1989 when SI featured outfielder Bo Jackson.
Greinke didn't seem too excited about the honor, according to The Star, which said he declined to sit for a portrait, prompting SI to use an action shot instead.
But his reluctance is not directed towards the magazine. Greinke simply just doesn't think it's a big deal.
"There's a lot more interesting stuff going on right now," Greinke told The Star, whose columnist, Joe Posnanski, will write the story chronicling Greinke's emergence as one of the game's premier pitchers despite a rocky start. "They should have something else on the cover. Playoff basketball or something else.
"So it's a mistake. They'll probably sell their least amount of magazines in a long time -- except when NASCAR was on the cover."
Greinke, a first-round pick by the Royals in the 2002 First-Year Player Draft, went 13-10 with a 3.47 ERA in 32 starts last season.
As for the SI cover jinx, the Orlando, Fla., native said he had never even heard of it.
"They have a jinx?" Greinke asked The Star. "Really, all that matters is winning games. Winning is what always mattered, but I would still like the other stuff. But now, I don't care one bit about it -- any of it, any award stuff, All-Star or anything."
Alden Gonzalez is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.