The right-hander will have surgery on a fractured bone in his right elbow, and could miss the season.
Floyd, who missed most of last season with Atlanta with the same injury, will have the operation on Tuesday at the Cleveland Clinic.
"He is certainly out for the foreseeable future," manager Terry Francona said. "I think more importantly rather than talking in March whether he can pitch in August or September are getting him healthy so he can proceed with his career. The safe presumption is that he will miss a significant portion, if not the whole year."
The club signed Floyd as a free agent in the offseason, hoping he could rebound and join their starting rotation. However, he experienced soreness before his spring debut and an MRI last week revealed the fracture.
Floyd went 2-2 in nine starts with the Braves before having surgery. He was limited to five starts in 2013 before Tommy John surgery. The 32-year-old Floyd won 65 games for the Chicago White Sox from 2007-13.
The injury to Floyd leaves three openings in the Indians' rotation.
"It was a big blow for us," McAllister said after his last start. "I played catch with him earlier this spring. We have depth though and a lot of talent. All of us have experience in the Major Leagues.
Marcum, who made the last of his 12 starts for the Mets on July 6, 2013, is a veteran getting a look from Francona.
"He is starting to get stretched out now," Francona said. "They are starting to pitch, facing hitters for a second time. Seeing how he bounces back is an important thing for us. We have a lot of intriguing options. Bruce (Chen), Marcum, both of them have been through it. The same thing with (Scott) Downs. We have some things to think about as we come into the last three weeks of camp."