The leg was severed at the scene and doctors in Rapid City performed the surgery.
He also underwent surgery to his hand.
In a statement posted at Wynonna.com, the couple expresses their appreciation for "all of the quick medical and police responders as well as the hospital staff and well-wishes from family, friends and fans."
Judd has canceled her concerts for the next week as a result of the accident. Her next scheduled date is set for August 30 in Michigan.