The on-loan Arsenal defender sustained the injury in the 2-0 win at Inverness last month.
Bartley may have to go under the knife after doctors diagnosed a hernia.
Rangers director of football Gordon Smith said: “Kyle has a hernia problem and we expect him to be out of action for between five and six weeks, although I’m not sure at this stage if surgery will be required. Either way, it’s obviously a big blow for the boy and the club.”
