Rasmus, who batted .276 with 22 home runs and 66 RBIs last season, was scheduled to hit seventh, but opted to sit as a precaution.
He does not expect it to be a long-term issue and hopes to return in a "couple days."
"I feel all right, I just woke up on the wrong side of the bed this morning," Rasmus said. "I got a little crick in my neck and it's just one of those things that after throwing and warming up, I just felt like I needed to take myself out."
Anthony Gose took Rasmus' place in centre field.