Teixeira is day to day and hopes to play in Sunday's rubber game.
"I'm going to get here early, get some treatment and see how it feels," he said, his thumb wrapped with gauze after the game.
"It's possible he'll play," manager Joe Girardi said. "We'll see. I hope so."
Teixeira suffered the injury on Friday night diving for a ball. He said his thumb jammed into the hard turf while he tried to brace himself.
It didn't bother him much on Friday -- he stayed in the game for his at-bat in the ninth, during which he was hit by a pitch -- but it was sore when he woke up on Saturday. The pain didn't go away in batting practice, but Teixeira was hoping the adrenaline of the game would carry him through.
"I thought adrenaline would kick in, but I had nothing," Teixeira said. "I tried to play through it, but I wasn't going to do the team any good."
Teixeira fouled out on his first at-bat on Saturday against John Danks, "swinging with one hand." Although he stayed in the game to play the field, he had already told Girardi that he wouldn't be able to hit the next time his turn came up.
Curtis Granderson pinch-hit for Teixeira in the third, with Nick Swisher moving in to play first base the rest of the night.
Teixeira has not missed a game due to injury all season. The only two contests he has missed were due to the birth of his son earlier this month.
Tim Britton is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.