"He's not going to play tomorrow, and I don't know if we'll see him in Seattle," manager Joe Girardi said after Saturday night's 2-1 loss to the A's. "(We'll) see how he responds to treatment."
Swisher, hurt trying to beat out a ground ball in the seventh inning on Friday night, said he was relieved the injury was not more serious.
"After hearing that it puts your mind at ease," he said. "You know exactly what you are dealing with."
Even if Swisher misses all three games in Seattle, a series starting Monday, the Yankees would be able to play a man short, Girardi said.
"We can do that if we have to," he said.
Dewayne Wise, who started in Swisher's place in right field on Saturday night, is a left-handed hitter. The Yankees will face all right-handed starters for the rest of the trip.