Teixeira, diagnosed with left wrist inflammation, underwent a cortisone shot and will be re-evaluated in three days, the team announced. X-rays taken Monday showed no breaks.
Teixeira said the best-case scenario is he'll be able to return to the lineup on Friday night against the Seattle Mariners. Until then, he'll continue to receive treatment and let his wrist rest.
"I'd love to be able to get here early on Friday and swing a bat and be able to tell (manager) Joe (Girardi) that I can play, but we'll see," Teixeira said. "We're gonna take it easy the next couple days, just treat it, and then we'll see where we are on Friday."
Teixeira first suffered the injury while swinging and missing right-handed in his third at-bat against Boston Red Sox left-hander Felix Doubront on Sunday night. He further irritated his wrist on Monday night while diving for a ground-ball single off the bat of Baltimore Orioles shortstop J.J. Hardy in the seventh inning, which forced him to leave the game.
Teixeira is hitting .256 with 20 home runs and 71 RBIs. In July, he is hitting .298 with seven homers and 27 RBIs in 24 games.
Teixeira, 32, is in the fourth season of his eight-year, $180 million contract.
Nick Swisher will start at first base and bat cleanup in Teixeira's absence on Tuesday night against the Orioles.
Teixeira suffered a similar injury in 2009, but received a cortisone shot and was fine after a couple days of rest.
"It's a little different, not as bad and it's in a different spot," Teixeira said. "(The doctors and I) actually even looked at that MRI and he showed me what I hurt in 2009. It's a similar injury, inflammation, sprain, whatever you want to call it, but it's in a different spot and treated the same. A couple days off, cortisone shot and then it never bothered me again."
Mike Mazzeo is a regular contributor to ESPNNewYork.com.