Kazmir felt sore after playing catch on flat ground during a team workout Monday. The Indians open the season Tuesday night at Toronto.
Manager Terry Francona said Kazmir will be reevaluated after he tries to throw a bullpen on Wednesday. The 29-year-old lefty was set to start Saturday at Tampa Bay.
Kazmir hasn't pitched in the major leagues in almost two years. A two-time All-Star with Tampa Bay, he was released by the Angels in 2011 and pitched last season in independent ball.
The Indians selected Kazmir for the 25-man roster and optioned left-hander Nick Hagadone to Triple-A Columbus. Cleveland also outrighted lefty David Huff to Columbus and had outfielder Ezequiel Carrera claimed off waivers by Philadelphia.