X-rays were negative, but an MRI revealed the strain. Yankees general manager Brian Cashman said in Tampa, Fla., that he was told Teixeira "felt a pop" in his wrist; as a result, Cashman said he expects Teixeira to be sidelined for a minimum of two weeks.
"I'm obviously worried about it," Cashman said. "Wrists are very unpredictable. Even if you can get a positive diagnosis back -- which of course we're going to hope for -- that still doesn't mean we're out of the woods, because wrists are tricky. They're hard to get a handle on."
Teixeira had already left the team and was not available to comment to reporters, but he said via Twitter, "Very disappointed to miss @WBCBaseball. Best of luck to my teammates, go #USA!"
Teixeira, who was supposed to be Team USA's starting first baseman throughout the Classic, was replaced at the position on Tuesday by Ben Zobrist, who batted ninth.
The Yankees said Teixeira was on his way to New York where he will be evaluated on Wednesday by team physician Dr. Christopher Ahmad along with Dr. Melvin Rosenwasser.
"He took three or four light swings as he was starting to get loose and he felt something in [his wrist]," Team USA manager Joe Torre said after the game, a 4-4 tie that was stopped at the end of regulation. "He had X-rays. The X-rays were fine, but an MRI showed a strain."
The Americans open their portion of the World Baseball Classic in Pool D on Friday against Mexico at Chase Field at 9 p.m. ET.
They have a second and final exhibition game on Wednesday night against the Rockies at Salt River Fields.
By game time on Friday, a replacement for Teixeira must be made on the 28-man roster. Although the names of Tigers first baseman Prince Fielder and White Sox first baseman Paul Konerko were floated, Torre said he, the coaches and team GM Joe Garagiola Jr. are just starting that process.
"We haven't reached out yet to anybody," Torre said. "We had a game to play and I'm not going to go into the players we were [previously] interested in. We're looking at a few options. But I don't think we're close to zeroing in on one guy."
Torre though, did say that he mentioned to White Sox manager Robin Ventura after the game that Konerko was a possibility.
"I just said that we're taking names of first basemen," Torre said. "[Konerko] just happened to get three hits off us today. That certainly is a consideration."
When Ventura was asked afterward if Konerko might be a consideration for the Team USA roster, he responded:
"It might be. It's about getting ready. If he's ready to go and play, it's his decision. He's been around long enough to know if it's going to help him or hurt him to be ready for the season."
Teixeira worked out with the team at Salt River Fields on Monday, the first day Team USA gathered, and didn't complain afterward about any problems.
"He said there was nothing. He never had this before," Torre said.
Torre said it was a shame that Teixeira had sustained the injury, particularly since he was so eager to be a part of the team. Torre said Teixeira told him he wanted to play when the two had a chance meeting during a charity event in New York this past December after Hurricane Sandy battered the area.
"We were sitting at the same table and he asked about the WBC," Torre recalled. "And I said, 'You're interested?' And he said, 'Yeah, if you need me, I'm interested, very much so.' And basically that was it. We just made a commitment at that point."
Teixeira missed a good portion of the last six weeks of the 2012 season because of a left calf injury. A notoriously slow starter at the plate, Teixeira said he had hoped that playing in the Classic would help jump start him this season.
Teixeira was previously a member of Team USA in the 2006 Classic, he was 0-for-15 and the U.S. didn't advance past the second round.