Bates was forced off early in the Old Firm defeat on Sunday after Celtic’s Tom Rogic inadvertently stamped on his ankle.
Murty says the 21-year-old hasn’t suffered a break, but he is unsure of the severity of the injury and he admits Bates may still face a spell on the sidelines.
He told RangersTV: ‘David is going to have a scan on his ankle, he has not broken it.
‘It is a freak injury, he steps to the ball and goes to try and make a block and the ball flicks off his shin which takes it out of Wes’ grasp and as Rogic has a shot he comes down on David’s ankle.
‘It looked a nasty one at the time and David is obviously upset but we won’t know the extent of it until we have it scanned.
‘He is off at the moment with his foot up, he has got a very fat ankle and we are very disappointed for him.
‘We are taking our time to make sure we get the assessment done properly and get a proper prognosis and a timescale in due course. We don’t know how long we have lost him for.’