Rookie Max Scherzer will get the start Sunday while Johnson heads back to Arizona to see team physician Michael Lee.
Johnson struggled in his last start on Monday, when he allowed five runs, including four home runs, in just 3 2/3 innings.
"I felt it in my last start against St. Louis, pitched through it and the results were what they were," Johnson said. "I felt like this might be the opportunity to get a little bit of a breather for my shoulder and then get it ready to finish the last four games that I have and then postseason."
Johnson played catch Saturday and said the shoulder felt better than it did Friday and if Sunday's game was the final one of the year and the D-backs needed him to pitch, he could and would. However, by skipping this start he will have 11 days between starts, which he thinks will be enough to allow the shoulder to recover.
"I just don't see [Sunday's] game outweighing the other four that I'm going to pitch and then possibly postseason," Johnson said.
Johnson is 10-9 with a 4.21 ERA in 26 starts this year, but has gotten better as the year has gone on. The Big Unit won five straight starts from July 6 to Aug. 1 and his only poor start of the second half was his last one against the Cardinals.
That Sunday is the first start Johnson has missed this season is remarkable given the fact that he's had two major back surgeries in the past two years.
"The bottom line is I'm pretty happy with the way the year has went health-wise," Johnson said. "Numbers-wise, obviously not."
Shoulder fatigue is not unique to Johnson, who is just six wins away from 300 and will turn 45 on Wednesday. He pointed to the Cubs right-hander Carlos Zambrano, who has experienced some shoulder issues recently.
"Sure," Johnson said when asked if he's had inflammation in his shoulder before. "I think everybody's gotten it. How old is Zambrano, 25 [actually 27]? He missed a start and I'm 45, so it's nothing to be too worried about. It's just stiffness, that's what inflammation is."
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.