General manager Ned Colletti announced the moves Sunday.
Kuo's injury, along with reliever Ronald Belisario's late arrival to spring training, opened spots on the 25-man roster for Monasterios and Ortiz, who hasn't pitched in the majors since 2007.
The Dodgers will carry 12 pitchers. The others are Chad Billingsley, Jonathan Broxton, Charlie Haeger, Clayton Kershaw, Hiroki Kuroda, opening day starter Vicente Padilla, George Sherrill, Ramon Troncoso, Cory Wade and Jeff Weaver.
Wade's inclusion comes as somewhat of a surprise, since he had surgery in mid-March to repair a frayed tendon in his right shoulder. The 26-year-old had a stellar rookie season in 2008, posting a 2.27 ERA in 55 appearances, but has dealt with shoulder problems since. He is expected to be placed on the disabled list Monday and replaced by Russ Ortiz, who boarded a team bus bound for the airport on Saturday.
Ortiz, a Los Angeles native who won 99 games from 1999 to 2004, finished the spring with a 2.50 earned-run average, striking out 15 batters and walking three in 18 innings.
Non-roster infielder Nick Green, who played 81 games at shortstop for Boston last season but hit only .139 this spring, will go to Triple-A Albuquerque.
Information from ESPNLosAngeles.com's Tony Jackson and The Associated Press contributed to this report.