Floyd left Saturday's 10-4 loss to Tampa Bay due to the injury after giving up two hits and two runs with two walks and a strikeout in 2 2/3 innings. He threw 47 pitches and departed after throwing a first-pitch strike to Evan Longoria.
Floyd had an MRI on Saturday night which did not indicate a tear. The right-hander is 0-4 with a 5.18 ERA in five starts.
"It can always be worse. In any situation, it can always be worse," manager Robin Ventura said. "We bring up guys that are capable of playing. Really, you look at it, you're going to get some guys opportunities. It's how we got [Jose] Quintana last year. There are opportunities that guys need to take advantage of. If it doesn't happen for us there is other teams looking at these guys for opportunities."
Floyd will be replaced in the rotation by Hector Santiago, who threw 86 pitches in relief Saturday. Floyd went on the DL last August with a similar injury. Santiago, 0-1 with a 2.51 ERA in seven appearances, will start Friday at Kansas City.
Deunte Heath was called up from Triple-A Charlotte to take Santiago's spot in the bullpen. He pitched nine scoreless innings for Charlotte in five appearances.