The 10th-ranked Longhorns' sophomore floor leader suffered the injury late in Thursday night's victory over Iowa when he drove to the basket, was hit by Iowa big man Gabe Olaseni and landed on his left wrist.
Taylor had his wrist heavily wrapped but told ESPN.com after the win that he did not think it was broken. Taylor received X-rays following the game.
"It looks like he's going to be out for several weeks," one source said, "but it's not season-ending."
Taylor is one of the top point guards in the country and averaged 12.7 points and four assists last season as a freshman.
He sat on the bench Friday with his arm in a sling and was replaced in the starting lineup by Javan Felix.