Badgers coach Bret Bielema said it will be determined after the surgery how much time Budmayr will miss.
The surgery is not expected to be season-ending.
Budmayr was Wisconsin's No. 1 quarterback this spring and entered preseason camp with a chance to win the job, but he began experiencing soreness in his right elbow Aug. 9. He later had trouble with a nerve that caused numbness in his throwing hand.
North Carolina State transfer Russell Wilson started Thursday night's opener against UNLV and led Wisconsin on eight scoring drives in a 51-17 win.
Budmayr's absence leaves Wisconsin with little depth behind Wilson. Joe Brennan will be the team's No. 2 quarterback.
Adam Rittenberg covers Big Ten football for ESPN.com. He can be reached at firstname.lastname@example.org.