Originally, Cruz was going to be bumped to Wednesday as long as his throwing session went fine, but he felt the same twinge, so a move was made.
Right-hander Dustin Nippert, who went 7-1 with a 3.47 ERA at Triple-A Tucson, was called up and will get the start Wednesday.
Russ Ortiz was moved up a day to fill the hole, and he took the loss after a six-week stint on the DL.
"[Cruz] has a little bit of lingering soreness in the back of his right shoulder," Diamondbacks manager Bob Melvin said before Tuesday's game.
Cruz originally felt a twinge in the fifth inning on May 27 against the Reds, but he went back out for the sixth inning before being pulled. Then, he fired seven scoreless innings against the Braves on Thursday.
"Since [the incident in Cincinnati], he has thrown the ball very well," Melvin said. "In his last bullpen [session], he felt it a little bit, and then [Monday night] he was sore."
Overall, Cruz is 3-3 with a 4.05 ERA after opening the year in the bullpen, where he had a 3.00 ERA in 12 innings.
Cruz didn't feel his last start was the cause.
"It was my longest [outing], but it wasn't too bad," he said. "I [had] been doing that in the Minor Leagues last year. We don't know [what the cause] is yet."
To make room for Ortiz on the roster, the Diamondbacks put left-hander Terry Mulholland on the disabled list with an inner ear infection.
Still waiting: Melvin said if there is a save situation Tuesday night, he probably will turn to Jorge Julio, because Jose Valverde pitched the night before.
Melvin intimated that Valverde would soon be back to his closer role.
"Julio has done a nice job in the interim," Melvin said. "In [Valverde's] last couple outings, he has done very well. He's had better pitch selection -- his command is better and a little less predictable. The last time out he was very good."
Wise approach: Shawn Green entered Tuesday's game with an 11-game hitting streak and ranked fifth in the National League with a .330 batting average.
The good start can be pinpointed to his ability to stay comfortable against left-handed pitchers. After hitting .226 in 146 at-bats against southpaws in 2005, the 33-year-old is at a .317 clip with three home runs and 10 RBIs in 63 at-bats this year.
"He's swinging better against left-handers and he has had some huge hits for us this year," Melvin said. "Sometimes as you get older, you have to make some adjustments, where it is results based and you are forced to do it. He's been great about it since Day 1 of Spring Training."
Minor matters: Outfielder Scott Hairston and left-handed pitcher Greg Smith have been named the organization's Minor League Player and Pitcher of the Month.
Hairston, 26, hit .379 in May with seven doubles, a triple, eight home runs and 29 RBIs for the Triple-A Tucson Sidewinders.
Smith, 22, won all six of his starts, posting an ERA of 1.62 for the Class A Lancaster JetHawks. Opposing batters hit only .188 off him, and he had 34 strikeouts in 39 innings.
Up next: The Diamondbacks will close the first series of a 10-game homestand on Wednesday. Cruz is scheduled to face Ryan Madson (5-3, 6.04 ERA) in a matchup of former relievers in their first year as Major League starters. First pitch is scheduled for 1:40 p.m. MST.