Parker was optioned to Triple-A Iowa, and infielders Baez and Chris Valaika, outfielder Casper Wells, and pitchers Brian Schlitter, Jonathan Sanchez and Chang-Yong Lim were assigned to the Minor League camp. The moves reduce the spring camp roster to 37.
Baez batted .310 with five home runs and five RBIs in 14 Cactus League games with the Cubs this spring, and ranked among the Major League spring leaders in home runs. He is projected as Triple-A Iowa's starting shortstop.
Parker, 28, who spent nearly all of last season in the big leagues after posting a 1.17 ERA in eight games in Spring Training, has given up six runs over six innings in six Cactus League games this year.
"He obviously did a nice job last year, and he's got to continue to command the zone and not make things too complicated and do what he does," Cubs manager Rick Renteria said. "He's got a tremendous arm."
Wells has been sidelined with back problems, and he underwent an MRI this week. Sanchez, 28, who threw a no-hitter with the Giants, was a non-roster invitee.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.