The Royals also optioned pitchers Miguel Almonte, the team's No. 4 prospect according to MLB Pipeline, and Kyle Zimmer, the team's No. 2 prospect, to Triple-A Omaha, along with Eibner and Martinez.
Right-hander Alec Mills, infielder Ramon Torres, Bonifacio and Starling were optioned to Double-A Northwest Arkansas.
Of the cuts, the only real surprise was perhaps Martinez, who had a shot for the final roster spot after winning the Pacific Coast League batting title (.384) last year. Martinez was having a decent camp (.278) as well.
"Right now, it starts to get tough to get those guys regular at-bats," manager Ned Yost said. "We need guys like Eibner and Martinez getting regular at-bats. Instead of getting four at-bats in five days, they'll get four at-bats every day down there [in Minor League camp]."
Zimmer has also had a solid camp, posting a 1.50 ERA in three appearances.
"I like the fact he was out there pitching and wasn't hurt," Yost said.
Jeffrey Flanagan is a reporter for MLB.com. Follow him on Twitter at @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.