Coach Gary Andersen said Tuesday Stave needs to rest. He has been dealing with the injury for a couple of weeks, and there is no timetable for his return.
Stave was the starter in 2013, when Wisconsin finished 9-4. He had an inconsistent season and hurt his right shoulder in the Capital One Bowl in January. The injury limited Stave during spring drills, and he lost the starting job to McEvoy after a preseason competition.
In a season-opening loss last week to LSU, McEvoy ran for 40 yards, but was 8-of-24 passing for 50 yards and two interceptions. The Badgers fell four spots in this week's AP Top 25 poll following the 28-24 loss to the Tigers after leading by 17 points.
McEvoy showed some promise carrying the ball. But the passing game struggled, especially in the second half. The Badgers also have inexperienced receivers.
Andersen's announcement Tuesday was the latest development at a position clouded by uncertainty all year. The Badgers hope their passing game can balance an offense headlined by star running back Melvin Gordon.
The depth chart released Monday for this weekend's home opener against FCS school Western Illinois listed McEvoy as the No. 1 starter for the first time. Still, Andersen said he thought there were opportunities for both Stave and McEvoy to play.
"We need two quarterbacks. Sooner or later you'll have to have them both. Tanner is the starter today, but Joel's going to fight like crazy to get some reps," Andersen had said.
Apparently, that's not going to happen for a while now.
"Joel has been dealing with some issues with his throwing shoulder for the last couple of weeks and we have come to a decision, after talking with Joel, that the best thing for him right now is to shut it down and give him some rest," Andersen said Tuesday.
"It was a tough decision because Joel is a great competitor and has a tremendous desire to help this team," he added. "We will continue to monitor his progress, but we're not putting a timetable on his return at this time."
As a third-year sophomore in 2013, Stave threw for 22 touchdowns and 13 interceptions last season and set a school record with 336 pass attempts. He threw for 2,494 yards and completed nearly 62 percent of his passes.
The 6-foot-6 McEvoy went to South Carolina for a year before transferring to Arizona Western College. A redshirt junior, McEvoy arrived at Wisconsin in 2013 and got moved to receiver before shuffling to safety following a wrist injury.
Wisconsin also has redshirt sophomore Bart Houston and dual-threat freshman D.J. Gillins at quarterback. Both were highly rated prospects.
Also Tuesday, Andersen said freshman tight end T.J. Watt would miss "extended" time after surgery - he injured his right knee in camp.
Watt is the younger brother of Houston Texans star J.J. Watt and Badgers fullback Derek Watt. Andersen hoped T.J. Watt would return to practice during the Big Ten portion of the schedule.
Andersen has also indicated that the injuries to senior defensive tackles Konrad Zagzebski and Warren Herring don't appear to be as serious as initially feared. LSU's increased success on the ground in the opener coincided with their departures.
Zagzebski was taken off on a stretcher as a precaution with a head and neck injury. Andersen said he could be back for this week's game, or by the Sept. 20 game against Bowling Green that follows a bye week.
Herring is considered day to day with a knee injury, and Andersen said he "should be back shortly."