The plan for Zambrano is for him to pitch out of the bullpen for Iowa until he joins the big league team in Denver the weekend of July 30th.
Zambrano pitched one inning and surrendered one hit on Monday in his only outing for the Cubs' Mesa, Ariz., rookie league team.
Zambrano has been on the restricted list since June 29 following a three-game suspension for an emotional outburst aimed at teammates in the dugout of a June 25 game against the Chicago White Sox.
In addition to his suspension and time on the restricted list, Zambrano is believed to have undergone anger management therapy with doctors picked by Major League Baseball and Zambrano's agent.
Zambrano does not have to be moved off the restricted list for a minor league stint, only if he is recalled by the Cubs.
Bruce Levine covers the Cubs for ESPNChicago.com