Pillar is expected to miss a week to 10 days with an oblique strain sustained while sneezing on Saturday morning.
Pillar, who is in contention for a starting spot, said he sneezed and felt a sharp pain in his right side, but opted not to tell team trainers about it until after he was pulled in the fifth inning of Toronto's win over a Yankees split squad. Following treatment, Pillar was advised to rest.
He did not play Sunday.
"I don't think this is a big deal," Pillar said. "It's something I played with (Saturday) and something I was prepared with to play today. But they're being very respectful about it and willing to give me a little bit of time."
Pillar is batting .269 with one home run and five RBIs in 26 plate appearances this spring.
"Just knowing how long obliques can linger," Blue Jays general manager Alex Anthopoulos told reporters. "I remember when Rajai Davis said he had a small one and could play through it. He did for another two weeks and then it got worse and he was on the shelf for about three weeks. Take the week, get it out of the way and he'll be fine."
Information from The Associated Press was used in this report.