Garcia was scratched from his scheduled start last Sunday due to a cut on his right finger that he suffered in a kitchen accident. A.J. Burnett started in Garcia's place.
With Garcia pushed back a day, it remains unclear if he will be able to pitch in the four-game series against the Twins, but it looks less likely than if he had thrown Thursday in the bullpen.
Girardi did not rule out Garcia pitching this weekend.
"I'm not sure when he's going to pitch again," Girardi said. "We just have to monitor his bullpen sessions. The big thing is we get him healthy and we get that finger ready. But it's a lot closer than it was."
Burnett will start again in Garcia's place Saturday, putting Ivan Nova would be in line to start Sunday's series finale.