With slightly more than three months remaining in the season, the only way Floyd can return this year is if he were to improve closer to the eight-week time frame.
"No surgery, but it's a long healing process," Blue Jays manager John Gibbons said.
Floyd was injured Saturday during a relief appearance against the White Sox. The 33-year-old veteran threw just two pitches before he had to come out of the game.
The injury is another blow to a Toronto bullpen that has struggled for most of the year. The Blue Jays' relievers entered Tuesday with an American-League high 18 losses and a 4.35 ERA that ranked 11th.
Floyd spent a brief period of time as a primary setup man for closer Roberto Osuna, but for the most part, he pitched in middle relief. He's also someone who had the ability to throw multiple innings out of the 'pen, and his versatility will not be easily replaced.
"I have no idea about that, but I know it's going to be a while," Gibbons said, when asked if Floyd was out for the season.
The good news for Toronto is that left-handers Brett Cecil and Franklin Morales are nearing their returns from the disabled list. Cecil is expected to return Thursday when the Blue Jays open a four-game series against the Indians, and Morales should be back around the same time.
Floyd has endured a string of bad luck with health. He has undergone multiple surgeries on his right elbow, and prior to this season, Floyd had not appeared in more than nine games since 2012.
"We're going to need some guys to step up," Gibbons said. "The good news is Cecil will be back soon. We'll be counting on him."
Gregor Chisholm has covered the Blue
Jays for MLB.com since 2011. Follow him on Twitter @gregorMLB and Facebook, and listen to his
podcast. This story was not subject to the approval of Major League Baseball or its clubs.