The injury was discovered by an MRI exam Wednesday. Floyd has been slowed by a sore knee since spring training and hasn't played since being scratched from the starting lineup Monday.
"Just started barking up again, just swelled up again," Floyd said. "I knew something was wrong. If it was feeling like this, it had to be something."
Floyd missed time last season with the Chicago Cubs because of neck, shoulder and elbow injuries. He has also spent time on the disabled list during his career because of ankle, knee and Achilles injuries.
"Here we are again," Floyd said. "Hopefully I can just come back and go from where I was going. Everything was going good."
Floyd is hitting .333 with two homers and five RBIs in four games. Rays manager Joe Maddon expects Floyd to be out four to six weeks.
Tampa Bay placed Floyd on the 15-day disabled list, retroactive to Monday. The Rays also recalled outfielder Justin Ruggiano from Triple-A Durham.
Rays pitcher Matt Garza, who went on the 15-day disabled list with nerve irritation in his pitching arm Tuesday, will not resume throwing until at least next week.
"I'll take it slow," Garza said. "I want to come back 100 percent. We don't want any setbacks. We'll take it day to day and see how it feels."
Maddon said Garza will be re-evaluated in two weeks and will be out a minimum of four weeks.
Rays ace Scott Kazmir, sidelined since late February with a left elbow strain, will throw a second batting session Friday or Saturday. He could pitch in an extended spring training game next week and might rejoin the team before the end of the month.
"He's doing great. He's doing well," Maddon said.