Pedroia is day-to-day, and will undergo precautionary X-rays on Wednesday.
The injury was sustained when Pedroia dove awkwardly for a ground ball by Twins leadoff man Denard Span in the bottom of the first inning. Pedroia made a throwing error on the play.
"When he went for that ball, it was the back of his wrist," said Red Sox manager Terry Francona. "He had mild effusion, which is limited swelling. We're going to get him X-rayed in the morning just to make sure. Their doctor came over [to check on him] -- I don't think there's a problem. He might be a little sore tomorrow. Hopefully that's all it is. He wasn't going to play tomorrow anyway. But we'll certainly get him checked up on."
Clay Buchholz was pitching for the Sox when Pedroia suffered the injury.
"I knew that when he came in, he was wincing a little bit," Buchholz said. "I asked him if he'd be all right. He said he'd be OK, but it was just precautionary, I guess, to get him out and take a look at it."
One of the best all-around second basemen in the game, Pedroia was the American League's Most Valuable Player Award winner in 2008. Last year, he hit .296 with 115 runs, 48 doubles, 15 homers, 72 RBIs and 20 stolen bases.
Pedroia went 0-for-1 on Tuesday. For the spring, he is hitting .351 (13-for-37) with one homer and eight RBIs.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.