Browne injured his right shoulder during last Saturday's 27-24 loss to Syracuse.
The injury ends the college career of the graduate transfer, who played at USC before joining the Panthers prior to this season.
"It's not a great thing for our program, it's not great for him, but he's hanging in there and he's good," Narduzzi said of Browne.
Sophomore Ben DiNucci will be the new starter, beginning with Saturday's game against North Carolina State.
Browne passed for 997 yards and five touchdowns against two interceptions this season. He completed 71.1 percent of his passes.
DiNucci is 36-of-65 passing for 442 yards, two touchdowns and two interceptions.