Cano said that he feels some tightness in the back of his right shoulder and Marte feels tightness in his left pectoral, setbacks that will keep both players out of action for New York this weekend.
The two are scheduled to be examined on Saturday by Yankees team physician Dr. Chris Ahmad in Tampa.
Yankees manager Joe Girardi said that he had planned on playing Cano in one of New York's games on Saturday, but the second baseman will instead be held out of action until a diagnosis can be made.
Cano said that he had felt some discomfort before reporting to the Classic club, but did not mention it to the Yankees.
"It was a little bit tight and it never went away," Cano said. "I can throw. It just feels tight. ... I was hoping that it was something that if I stretched, it'd be all right."
Marte said that he felt the tightness after performing bench presses prior to Tuesday's game, when he pitched an inning in the Dominican Republic's 2-1 loss to the Netherlands.
Marte said that the tightness did not affect him on the mound and estimated that he would need to rest three or four days.
"I'm good," Marte said. "It's just a little bit tight."
Girardi said that the higher level of competition in the Classic may have been a contributing factor.
"What happens is, you go to those games and your intensity is really turned up a lot sooner than it would be normally," Girardi said. "Hopefully it's not much and they bounce back fairly quickly, but it's not how you want them coming back."
The Dominican Republic suffered a stunning defeat when it lost to the Netherlands in Game 5 of Pool D play on Tuesday, falling in extra innings.
"I was so disappointed -- I thought we were going to make it to at least the second round," Cano said. "That's the game of baseball. We'll just take it to the next time. We didn't hit that well."
"That's baseball," Marte added. "If you don't hit, you don't win."
Cano said that having Alex Rodriguez in the lineup would have helped. Regardless, Cano believes the star-studded Dominican Republic roster should have put on a better show, considering the competition.
"Those guys had guys from [Class] A ball and Double-A," Cano said. "I would say we should have beat them. This is the game of baseball. You never know what's going to happen until the last out.
"If they'd told me that before, I might laugh. With those guys that we've got, that's hard to believe. We've got 23 Major Leaguers and [The Netherlands had] two -- Sidney Ponson and Randall Simon."
With the Yankees already patching holes from within for the extended absence of A-Rod, Girardi said that he had not given any thought to the idea that Cano might also be subtracted from the lineup.
"I'm not sure what we would do," Girardi said. "I don't think it's long term. I think he'll be out a couple of days."
Cano batted .231 (3-for-13) with two runs scored and one walk in three games for the Dominicans, while Marte made two relief appearances, throwing two scoreless innings.
In addition, Francisco Cervelli returned to camp on Tuesday after batting .143 (1-for-7) with a run scored and a walk in three games for Italy.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.