"Not great news out of Tampa today," Yankees manager Joe Girardi said.
Molina felt another twinge in his strained right quadriceps after notching a hit in an extended spring training game and had to be removed from the contest.
Molina had been intended to catch five innings for the first time since he went on the disabled list on May 10, and he is scheduled be re-evaluated by the Yankees' medical staff.
Additionally, Nady felt discomfort in his right elbow as he threw for the first time since he was injured making a return throw to the infield on April 14 at Tampa Bay. Girardi said that Nady was throwing from distances of 50 to 60 feet and did not immediately have any trouble, but he felt discomfort near the end of his session.
Nady, who is trying to avoid season-ending Tommy John surgery, will throw again tomorrow.
The Yankees had hoped to have Nady with them as an outfield option by the time New York plays in Interleague games at National League parks beginning June 19, but Monday's news made Girardi less confident that it would actually happen.
Nady could potentially serve as a designated hitter, as he does not feel pain when hitting, but the Yankees already have a dedicated DH in Hideki Matsui. Finding at-bats for Nady would be difficult if he can't be counted on for at least some defensive duty.
"It makes it tough if he can't, in a sense," Girardi said. "My thought is that you don't have to throw it far. You can run the second baseman out there further. But you have to have some flexibility. It's tough on Matsui if he's running around there and his knee blows up. Who's more likely to do that and stay healthy? We don't know."
There was a third bit of negative information as left-handed reliever Damaso Marte stubbed a pinky toe, though it did not keep him from his regular throwing session.
The only good injury-related news came on-site in Cleveland, where Melky Cabrera returned to New York's lineup after suffering a bruised right shoulder while crashing into an outfield fence in pursuit of Ian Kinsler's leadoff triple on Tuesday at Texas.
"I was concerned that he was going to be out for a while, the way that he walked off the field," Girardi said. "I thought it would be a DL situation. Whenever you hit your shoulder like that, you worry about a separation. But he's come back really quickly, and that's good for us."
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.