The City full-back, who has been sidelined since sustaining the injury during the 3-2 away win at Barnsley at the end of October, had hoped to have recovered in time for this weekend's clash against West Brom.
However, manager Gary Johnson has confirmed that Orr will not be fit in time for the trip to The Hawthorns on Saturday.
"It is likely he will be out of action for at least another seven to ten days," Johnson told the club's official website.
"We had hoped that he would be back in training and in contention for the West Brom game this week, but that has not happened.
"No one is more disappointed than Brad, because he thought he was on the way back."