McCarthy is 2-4 with a 5.00 ERA in 11 starts this season. In 3 starts from May 12-24, he went 2-0 with a 0.38 ERA including a career-high 18-inning scoreless streak from May 7-24.
He struggled on Thursday, giving up six runs on nine hits in 2 2-3 innings.
"We knew going into last game he wasn't feeling great," said Diamondbacks manager Kirk Gibson. "He's had a history, so after his start he wasn't feeling very good. You ask yourself whether you want to push through, is it going to happen now, is it inevitable? With his history we just thought the best course was to stop it right now."
McCarthy's 2012 season was cut short Sept. 5, when he was pitching against the Los Angeles Angels and was struck in the head by a line drive. McCarthy, who was pitching for the Oakland Athletics at the time, had surgery after suffering a fractured skull and an epidural hemorrhage.
McCarthy has been placed on the disabled list eight times in his career for various injuries and is quite familiar with shoulder issues.
"It's getting less frustrating and more used to it, as annoying as that is," McCarthy said. "At least you take away a lot of the unknown. I know what the recovery is, I know how long it takes for the whole thing. I know what I'm feeling for, that makes it a little easier, I'm not as worried. The fact that I still can't figure out how to get around it or what it is, that's kind of the difficult part."
McCarthy is scheduled for an MRI on Monday to confirm there is no unexpected damage to his shoulder.
In 11 starts with Reno, Delgado was 1-4 with a 6.84 ERA. This is his first stint in the majors this season. In 2011-12 with the Braves, he appeared in 25 games (24 starts) and went 5-10 with a 3.95 ERA.
Gibson said the team would see how the next three games go before deciding who would start in McCarthy's spot on Tuesday, indicating that both Delgado and Tyler Skaggs were options.
In his only big league start of the season on Monday against the Texas Rangers, Skaggs tossed six shutout innings, allowing only three hits while striking out nine and walking three. Skaggs is currently at Reno, where he is 4-5 with a 5.23 ERA with 54 strikeouts and 17 walks in nine starts.