Andersen said Watt had knee surgery and "will miss an extended amount of time, but we hope to have him back on the practice field at some point during the conference season."
Stave is "dealing with some issues with his throwing shoulder," and will be shut down to allow him to rest, Andersen said. He said there is no timetable for the quarterback's return.
Neither Watt nor Stave saw action in the Badgers' season opener against LSU.
Wisconsin hosts Western Illinois on Saturday.
- Dan Gartland