Swisher worked a walk in the third inning against Tigers right-hander Max Scherzer and, while at first base, grabbed at the back of his left leg as though he was trying to work out tightness.
An MRI taken during the Yankees' 6-2 victory over the Tigers revealed the strain. Girardi said that he did not know if Swisher would require a stint on the disabled list.
"He's got a real low-grade strain," Girardi said. "We're probably looking at more than a few days, but I'm not saying it's a DL [situation]. We'll have to see how it progresses in the next few days."
The injury puts a damper on what has been a very positive April for Swisher, as the switch-hitter has totaled 23 RBIs, including slugging homers from both sides of the plate in Saturday's 7-5 loss to the Tigers.
Girardi said that he did not anticipate the Yankees calling up another outfielder before Monday's game against the Orioles, and mentioned that Brett Gardner is eligible to return from his right elbow strain on Thursday. If the Yankees summoned an outfielder from Triple-A Scranton/Wilkes-Barre, veteran DeWayne Wise would figure to be first in line.