Rasmus had been scheduled to play center field and bat seventh against the Yankees but instead received permission to take the day off.
"I feel all right, just woke up on the wrong side of the bed this morning," Rasmus said. "I have a little crick in my neck. ... I felt like I needed to take myself out just as a precaution. But in a couple of days, I should be fine."
The injury news for some of the other position players was a little more positive. Edwin Encarnacion and Brett Lawrie were back in the lineup just one day after being scratched because of various ailments.
Lawrie was held out of Saturday afternoon's game against the Orioles because of a tight hamstring. Encarnacion received the past two days off as the Blue Jays took a cautious approach following last September's surgery on his wrist.
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, and follow him on Twitter @gregorMLB. This story was not subject to the approval of Major League Baseball or its clubs.