"We're going to kind of go the cautious course," Indians manager Terry Francona said.
The Indians will announce a replacement starter on Thursday. Candidates from Triple-A Columbus include Corey Kluber and Trevor Bauer -- both of whom are on the 40-man roster -- and Daisuke Matsuzaka, who is not. Righty Carlos Carrasco is not an option because he is currently serving a six-game suspension.
The Indians are sending Kazmir back to Cleveland, where he will undergo an MRI exam to determine the extent of his injury. The current plan is to have the pitcher rejoin the ballclub on Friday for its road series against Tampa Bay.
Kazmir alerted the Tribe's medical staff to some discomfort in his right side after playing catch on flat ground at a distance of 90 feet on Monday. Prior to Wednesday's game against the Blue Jays, the 29-year-old lefty worked through a 30-pitch bullpen session without any issues.
"It was pretty important," Kazmir said of his mound session. "As soon as I felt a little something, it was very minor to begin with. To be able to throw this bullpen pain-free, it felt good."
Kazmir said he felt well enough to pitch Saturday, but added that he understood if the team wanted to delay his season debut.
"He did fine. He did well. He probably could've pitched," Francona said. "The kid has worked hard. He made the club. It just didn't seem to make sense to any of us to [have him pitch Saturday]. We were really encouraged by the way he threw. We just didn't think it made sense."
Kazmir, who has not pitched a full season in the Majors since 2010, earned the fifth spot of the rotation as a non-roster invitee this spring, allowing nine runs (eight earned) on 29 hits with 23 strikeouts and only three walks in 21 innings, which covers four Cactus League appearances and a pair of Minor League outings.
If Kazmir needs a stint on the disabled list, Cleveland can back-date it to Tuesday, meaning he would be eligible to be activated on April 17.
Jordan Bastian is a reporter for MLB.com. Read his blog, Major League Bastian, and follow him on Twitter @MLBastian. This story was not subject to the approval of Major League Baseball or its clubs.