Kingsley, a permanent signing from Swansea in the summer, sustained the injury in the recent home defeat to Preston.
“Stephen had an operation in Munich on Wednesday and he maybe needs four weeks to recover. He will only come back after the international break in November,” head coach Leonid Slutsky told the club’s official website.
Max Clark stepped in for Kingsley at left-back in the 6-1 win against Birmingham last time out and will provide cover during the latter’s rehabilitation.
Kingsley has made five appearances for the Tigers since the club paid an undisclosed fee to sign him from Swansea in August following Andrew Robertson’s departure to Liverpool.