The White Sox placed Floyd on the 15-day DL Tuesday and activated right-hander Philip Humber, who is to start Tuesday night against the Red Sox.
Floyd had been hopeful of avoiding the DL.
"If we get this under control and minimize the inflammation, I guess we can hopefully get right back and not miss much," he had said.
"From what I'm understanding, we are going to give it a break so it calms down. But I don't know. I haven't heard anything. We are taking one day at a time."
With Floyd out of action, Dylan Axelrod moved up one day to start Monday. Jose Quintana closes out the four-game set Thursday night, with Jake Peavy and Chris Sale opening the weekend series against Detroit at Comerica Park.
Starters for Wednesday and Sunday remain undecided, although left-hander Pedro Hernandez stands on schedule with Triple-A Charlotte to work in the third game against Boston. That topic is under discussion between manager Robin Ventura, pitching coach Don Cooper and general manager Ken Williams.
"You have to make a move whether Gavin goes on the DL or not," said Ventura, referring to Humber's return Tuesday. "It's more of how [Floyd] is feeling."
Soreness for Floyd heightened during his last start on July 7 against the Blue Jays, with it becoming more noticeable on the torque of his off-speed pitches, and he felt it again while playing catch over the All-Star break. It was a Friday bullpen session in Kansas City that made Floyd take action.
"I was like, 'I don't think I'll be able to go more than warm-ups and without it potentially getting worse,'" said Floyd, who didn't want to pitch, worried that something was wrong. "I threw the next day after my bullpen on flat ground and it felt pretty good.
"It was just, I was getting mixed signals but I had to go off what I threw off the mound because it takes more torque off the mound. We took an MRI just to be cautious."