Thames strained his right hamstring in Saturday's 9-3 win over the Astros and was replaced by Brett Gardner in leftfield after four innings.
An MRI was negative, but Thames will be out at least 15 days. The Yankees will add a player before Sunday's series finale.
Manager Joe Girardi said he was not sure when Thames was injured.
The Yankees led 6-2 when Girardi pulled Thames, who went 0-for-1 with a walk and is batting .276.
Thames was involved in one play: Jeff Keppinger's third-inning double into the leftfield corner that scored Tommy Manzella from first base.
Thames failed to cut off the ball before it went to the wall and threw high to Jeter on the relay attempt. Jeter dropped the ball as any chance to make a play on Manzella was lost. No error was charged.
Gardner made his first appearance since leaving Tuesday's game in Baltimore with a sore left thumb. He went 0-for-2 and should be in the lineup Sunday.
Robinson Cano fouled a pitch off his right shin in the seventh inning, but stayed in and said he expected to play Sunday.
Girardi said Alex Rodriguez "felt better" with the tendinitis in his hip flexor. He is not expected to play before Tuesday.
"We'll evaluate day to day," Girardi said. "We'll put him in when we feel that he's ready. Obviously, it's good to hear that he felt better. That's encouraging to me."
Position: Left out
Kevin Russo filled in for Rodriguez at third base and went 1-for-4. In the field, he was not involved in a single play.
The only time he touched the ball was "when it was thrown around the infield," Russo said.
With Javier Vazquez's win, the Yankees, for the first time since 1939, have five starters with at least six victories in the team's first 62 games, according to Elias . . . The Yankees have won seven straight home games.