He will undergo surgery Friday morning by Dr. Coco Eaton, and the Rays estimate he will out 2-4 weeks.
Floyd said the MRI was his second this spring and after he cleared the first test, he thought the pain would subside.
"You hope you can play through it, because it was painful -- but I've dealt with worse pain than that," Floyd said. "I'm pretty much speechless ... I'm here in a great situation with a great team."
Floyd, who was a last-minute scratch in Monday's game in New York, told the media on Tuesday that his knee was feeling fine. Maddon also noted Tuesday that Floyd was dealing with some right-knee soreness but didn't offer any indication that it was anything serious.
The results from an MRI late Tuesday night suggested otherwise, and were a major setback to an already injured Rays team. Floyd joins Kazmir, Garza, Dioner Navarro, Ben Zobrist, Rocco Baldelli, Kurt Birkins and Chad Orvella, on an already crowded disabled list.
To replace the roster spot, the Rays recalled outfielder Justin Ruggiano from Triple-A Durham in Floyd's absence. Ruggiano, along with Durham teammate Jae Kuk Ryu, arrived Wednesday afternoon after a frenzied night of travel. Ruggiano and Ryu were at Buffalo Wild Wings in Columbus eating dinner with teammates Jeff Niemann and Mitch Talbot when their respective cell phones went off.
"I asked them, 'Can I smile?'" Ryu said of the awkward moment experienced when half of the table was ecstatic. "The guys were talking about Garza being hurt, so we all assumed Niemann would get the call."
Niemann still might. After Maddon confirmed that Ryu would be used mostly to shore up a tired bullpen that went a combined 6 1/3 innings Tuesday night, he coyly mentioned it was "possible" for the team to call up another player for Garza's scheduled start Sunday. Niemann, a lanky righty, would be a perfect fit since he received a favorable amount of innings in Spring Training and is already scheduled to pitch Sunday for Durham.
Ryu and Ruggiano, among the first cuts in Spring Training, both said the injuries were unfortunate, but they were eager for the Major League opportunity.
"I was disappointed, but I knew they had a plan and whatever it was they were going to stick by it," Ruggiano said. "And I was the first one called up. So I just got to go out there and show them what I can do right now."
Ruggiano was batting .304 in Durham, including a 2-for-4 appearance in Tuesday night's win over Columbus.
Floyd was also riding a hot streak. The Rays designated hitter was signed as a free agent in the offseason and hit .333 with two home runs in his first 15 plate appearances. The usually charismatic Floyd was visibly upset to be shelved, saying he felt after a sluggish spring that his bat was beginning to come around.
"When you have a guy like him in the lineup it just makes everyone else around him better," Maddon said.
Floyd's powerful lefty bat sitting behind right-handed hitter B.J. Upton and followed by Eric Hinske's left-handed swing gave the Rays a firm middle lineup vs. right-handed pitching.
For now, Maddon said the Rays will likely substitute Nathan Haynes in right field in Thursday's matchup against righty Miguel Batista, with Hinske or Jonny Gomes as the designated hitter.
Brittany Ghiroli is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.