Kazmir has been slowed by a left elbow strain, which he felt while warming up for an intrasquad game on Feb. 26.
"It will definitely knock out the Opening Day assignment," Rays manager Joe Maddon said before Saturday's split-squad game against the New York Yankees. "We just want him to try and build up a little bit more arm strength before we put him back out there. He's fine. There's not a thing wrong with him. During the season he probably would have pitched today."
Kazmir was scheduled to play catch on Saturday.
"Then he'll go back on the mound again, and then when I'm satisfied we'll put him into a game," Maddon said.
James Shields will replace Kazmir against the Tigers on Sunday, and could pitch the regular-season opener.
Kazmir, the AL strikeout champion, went 13-9 with a 3.48 ERA last season.
Rays left fielder Carl Crawford didn't play Saturday because of tightness in both his legs. He might return Sunday or Monday.
"He just came up a little tight today," Maddon said. "I just think the field was kind of wet yesterday, and sometimes you run on soft ground it can happen."