The injury occurred during the ninth inning of Friday's 4-3 win at Kauffman Stadium. Santos picked up the save, allowing one run to score, but felt some tightness, according to manager John Farrell.
"He didn't feel quite right in that save situation last night," Farrell said after Saturday's game. "And as the evening progressed, he felt more tightness throughout the night. He woke up [Saturday] morning with that inflammation kind of rearing its head."
Santos said he was able to continue pitching on Friday, but things acted up Saturday.
"I felt OK, and then at some point in that inning I just could kind of feel that something wasn't quite right," Santos said on Saturday. "It wasn't that bad. I could kind of fight through it, and then I woke up [Saturday] morning and it was barking pretty good. I came in and let the staff know. Their thought was let's get this over with and not have it drag on, so let's shut it down now and hope that we can catch it early."
Farrell said the move is precautionary to make sure that Santos is at full health later in the season.
"If we're in the seventh game of the World Series," Farrell said, "he's pitching, but given the fact that where we are in the season, we don't want to take any chances with this."
Farrell said that Francisco Cordero will serve as the team's closer while Santos is out.
The club announced that right-handed pitcher Evan Crawford will be recalled from Double-A New Hampshire on Sunday. Crawford has already appeared in two games for the Blue Jays this season, allowing zero runs, one hit and three walks in two innings.