Floyd was placed on the 15-day disabled list Monday, retroactive to April 5, with a strained right shoulder.
"Cliff had an injection the other day for an MRI," said Black. "His shoulder is a little sore from that. But he still has another nine days or so to get back in the swing of things."
Black said that MRI didn't reveal anything new.
"I would think that Cliff would have to face some live pitching at some point and would need a rehab assignment," said Black.
Floyd strained his right shoulder in a Spring Training game against the Cleveland Indians on March 25, when he took a big swing at a changeup low and away from Indians pitcher Carl Pavano. The shoulder tightened on him shortly thereafter, and he left the game.
Floyd, who had shoulder soreness earlier in camp, underwent tests by Padres doctors in Peoria, Ariz. Nothing substantial was found, and Floyd rested the shoulder. He missed six games.
Floyd played in the Cactus League finale against Seattle on April 2. He then pinch-hit in an April 3 exhibition game against the Angels and had two at-bats April 4 in another game against the Angels in Anaheim.
In another injury update, Black said that pitcher Cha Sung Baek, who also has missed the beginning of the season, "is coming along."
Baek suffered a strained right forearm March 29 against the Dodgers and has been on the DL.
"He's been playing catch and lengthening out, and we'll be getting together with Todd [Hutcheson, athletic trainer] and Darren [Balsley, pitching coach] and map out a game plan here as far as when he's going to throw in the bullpen," said Black. "We're talking about the latest part of April. He's progressing very well."
Sandy Burgin is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.