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.