The Indians will put Giambi on the disabled list formally Sunday.
Giambi was diagnosed with a broken rib in his right side March 13 and was expected to be sidelined about three to four weeks. He had been hit by a pitch thrown by Edwin Jackson of the Chicago Cubs in the third inning of a March 7 game. X-rays at the time were negative, but Cleveland said the 43-year-old Giambi felt increased discomfort over the ensuing days.
The 2000 American League MVP, Giambi was a nonroster invitee to big league training camp. The designated hitter hopes to play in his 20th major league season and second with the Indians.
The Indians previously expressed hope that he will rebound and be in position to join the big league team later.
"It is why you try to evaluate everybody, because if you need a plan B or a plan C, you have it," manager Terry Francona said.
The Associated Press contributed to this report.