An Arkansas State spokesman said Bonner had surgery on his right hand Wednesday.
Bonner, a junior, led the Sun Belt Conference with 1,052 yards passing in four games and had 10 touchdown passes to one interception. He led the Red Wolves to a 2-2 start, including a close loss to SMU.
Bonner said in a Tweet that he tried to play through the injury but he "physically can't go anymore."
Arkansas State coach Blake Anderson has announced former Alabama quarterback Layne Hatcher as the starter for Saturday's game against Troy. Hatcher is Arkansas high school football's career leader in yards passing and passing touchdowns. He led Pulaski Academy to three state titles.