Garcia, a veteran right-hander, was scratched from his Sunday start due to a cut on his right finger he suffered in "a kitchen accident," according to manager Joe Girardi.
A.J. Burnett will start in place of Garcia on Sunday against Tampa.
Garcia's injury leaves the Yankees with five healthy starting pitchers, instead of the six they'd been using for the past two weeks.
Thus, they can avoid having to cut one starter from their current six-man rotation to get it down to five.
Girardi had planned to cut the rotation down from six starters to five by Monday.
The decision was likely going to come down to demoting either Phil Hughes or Burnett.
And it would have been that much more difficult to make after Hughes allowed two runs in six innings in a win over Tampa on Saturday evening.
But Garcia apparently made the call for the Yankees when he cut his finger "about four or five days ago," according to Girardi.
"Sometimes decisions have a way of working their way out," the manager said, adding that he is "not sure" when Garcia will return.
"It's not real deep but it's where he throws his (split-finger fastball) and it rubs on the side of the finger, so the decision was made," he said.
Garcia made it through a bullpen session earlier this week without throwing the splitter. According to Girardi, Garcia tried to throw the pitch on flat ground Saturday but the cut was too much of an impediment. Girardi said he hopes Garcia misses just one start.
"But obviously we've got to make sure it's healed before we have him even try," the manager said. "And he's going to have to throw a bullpen before he even tries to pitch in a game."
Garcia, a 35-year-old journeyman the Yankees signed to a minor league contract in spring training, has a 10-7 record and 3.16 ERA through 20 starts in 2011.
"We'll see what happens," he said.
Over the past two weeks, there has been a rancorous debate among Yankees fans and observers over which starter should be demoted to create a five-man rotation. Hughes and Burnett seemed to be the prime candidates. Before Friday's game, GM Brian Cashman launched an impassioned defense of Burnett, the enigmatic right-hander who has been a lightning rod for Yankees fans.
"We got six guys that are capable of pitching in a rotation in a playoff race and that's a good thing, so somebody has to go and we're going to make that decision, but this stuff about (how) A.J. Burnett is worthy of being ripped from the rotation is a bunch of crap," Cashman said.
With Garcia's injury, the Yankees can now avoid any public outcry over the demotion.
"There's so many times in this game that things have a way of working (themselves) out," Girardi said. "Phil threw a very good game today and we'll just keep going and see what happens."
Ian Begley and Mike Mazzeo are frequent contributors to ESPNNewYork.com.