"You're probably looking at a month," Girardi said. "It's one thing if you're a DH who doesn't run extremely fast, but when you're a center fielder, it takes some time. I hope it's less than that."
Granderson suffered the injury in the sixth inning on Saturday. The center fielder was stealing second when Brett Gardner singled to right field, forcing him to quickly change his angle and reach a little too far for the bag.
"I was stealing second, and my angle was to steal the base," Granderson said. "I had to get deep, and I ended up reaching for second base. As soon as I did that, I felt a grab right in my groin area -- no pop, no snap, just a grab."
Granderson compared the feeling to that of a cramp, which allowed him to hop his way safely to third base. He added that it felt a lot better on Sunday than it did on Saturday, that there isn't much swelling and that he feels pain only during certain movements -- such as changes of direction and stepping sideways.
"It definitely could be worse," Granderson said. "Ankle, knee, Achilles -- it could be a lot longer than this."
Granderson will miss the Yankees' upcoming road trip, which includes the team's only stop in his former digs in Detroit this season.
"I was looking forward to it, getting the chance to go back there and play," Granderson said. "Hopefully I can still go. I have a lot of friends and family coming up from Chicago."
In Granderson's absence, Gardner will move over to center field with Marcus Thames and Randy Winn splitting time in left. Thames was in the starting lineup on Sunday against White Sox left-hander Mark Buerhle. Winn is likely to earn more time against right-handers.
The team called up right-handed reliever Mark Melancon to take Granderson's spot on the roster, although that is to fill a short-term need.
"Right now, we're going with a 13th pitcher," Girardi said, adding that Melancon was the most rested reliever at Triple-A Scranton/Wilkes-Barre. "Until we feel that our bullpen is back, because we used our two long men yesterday, we'll do that."