They replaced Philadelphia’s Bryce Harper and Houston’s Yordan Alvarez, who are hurt, and Milwaukee closer Josh Hader, who is skipping the July 19 game at Dodger Stadium because of family responsibilities.
Rodon made the All-Star team for the second straight season. He is 8-5 with a 2.70 ERA in 17 starts, striking out 124 and walking 32 in 100 innings.
Martinez, 34, is a five-time All-Star who is hitting .313 with nine homers, 38 RBIs and 29 doubles, tied for the American League lead. He earned a $100,000 bonus for his selection.
Cooper, 31, becomes the 31st first-time All-Star this year. He is batting .299 with seven homers and 40 RBIs.
Martinez and Cooper each were next in player voting. Rodon was selected by Major League Baseball.
Hader spent a week on the paternity list in June after his son, Lucas, was born. His wife, Maria, had complications with her pregnancy.
“A lot on his plate, for sure, these last six weeks,” Brewers manager Craig Counsell said in Minneapolis before a two-game series against the Twins. “The All-Star Game’s a great honor, and it’s not an easy choice.”
Said Hader: “I think my duty is to be with my family, and I think just to be ready for the second half. My family needs me at this time, and that’s just kind of the decision that we made.”
Harper was elected as the National League’s designated hitter but broke his left thumb when hit by a pitch from San Diego’s Blake Snell on June 25. He was replaced in the starting lineup by Atlanta’s William Contreras.
Alvarez went on the injured list because of a ailing right hand that has gotten worse since he first got hurt June 18 against the Chicago White Sox.