"I don't think it's a big issue," Darvish said. "But just as a precaution, I would rather skip a start than push it through."
Darvish was scheduled to pitch on Thursday against the Orioles. He will be replaced by reliever Ross Wolf, and Joseph Ortiz will be called up to replace Wolf in the 'pen. Wolf is 1-1 with a 1.95 ERA in one start and nine relief appearances since being called up from Triple-A Round Rock.
"We feel like he can get the job done for us," manager Ron Washington said.
Darvish, who last pitched on Saturday against the Astros, first felt the muscle bothering him on Monday during his between-starts throwing session. He played catch on Wednesday and continued to feel the discomfort in the shoulder. That's when the Rangers decided to shut him down.
"At this stage, it's not something we're worried about," assistant general manager Thad Levine said. "If we sit him down for two weeks and miss one start, it's better for Darvish and he can hit the ground running in the second half. He is characterizing it as a fatigue type of deal more than anything."
Darvish was elected to the American League All-Star team in the players' vote. He is still planning to attend the game, but he will not be able to pitch. He is eligible to come off the disabled list on July 22, and the Rangers are expecting him to pitch that night against the Yankees.
"When I came in, I had a message from Ron Washington that Darvish was on the disabled list," Tigers and AL All-Star manager Jim Leyland said. "Since it's a pitcher it'll be my pick, and I'll just have to go back to my laptop and what do you call it, the iPad, and go to work."
The Rangers now have four of the five members from their Opening Day rotation on the disabled list, as Darvish joins Alexi Ogando, Matt Harrison and Nick Tepesch. Colby Lewis and Neftali Feliz -- who were in the rotation on Opening Day in 2012 -- are also on the disabled list.
Ogando, who is on the DL with shoulder inflammation, is scheduled to make a second start on a medical rehab assignment for Round Rock on Thursday. He will likely make another start in the Minors next week and also be ready to rejoin the rotation after the All-Star break. Tepesch was placed on the disabled on Saturday with elbow inflammation and has not resumed throwing. Harrison, who had back surgery, won't be back until the end of August at the earliest.
Darvish is 8-4 with a 3.02 ERA in 18 starts this season, and he leads the league with 157 strikeouts. He has averaged 109.5 pitches, the most in the AL. His 1,971 pitches are the seventh most thrown by a pitcher in the league.