The injury was announced about 10 minutes before first pitch.
The Yankees also lost Anthony Rizzo after he collided with Fernando Tatis Jr. on a pickoff attempt at first base in the top of the sixth. Rizzo was removed from the game ahead of the seventh inning for "precautionary reasons" after suffering a neck injury in the collision, but Yankees manager Aaron Boone said Rizzo was "fine" after going through tests postgame.
Soto, meanwhile, was held out of the starting lineup for the first time this season and replaced by José Azocar. Soto was set to bat third in San Diego's original lineup, and Xander Bogaerts moved to that spot after not starting Saturday because of wrist soreness.
"I wasn't comfortable, he's played so much here and he had some stiffness," Padres manager Bob Melvin said. "I just wasn't comfortable with that. We figured we'd take one swing with him at some point in time."
Soto came up as a pinch hitter and grounded out in the ninth against Clay Holmes, ending his 11-game on-base streak.
Melvin said he expects Soto to start Tuesday's series opener against the Marlins.
Soto hit a two-run homer Friday in a 5-1 win after fouling a pitch off his left knee. He hit a 432-foot drive to right field that came off the bat at 114 mph, the Padres' hardest-hit home run this season.
Soto is batting .263 with 10 homers and 24 RBIs in his first full season with the Padres, who acquired him from Washington at last year's trade deadline. He went 0-for-2 with two walks Saturday in a 3-2, 10-inning loss to extend his on-base streak to 11 games.
The Associated Press contributed to this story.