The 21-year-old had attempted to block Tom Rogic's equaliser before the Hoops midfielder accidentally landed on the defender's ankle after connecting with the ball.
Bates was stretchered off amid fears that he had suffered a fracture, but the Rangers boss admitted that this was not the case, although a precautionary scan will still be carried out.
"David is going to have a scan on his ankle, he has not broken it," Murty told Rangers TV.
"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 [Foderingham's] 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."
Bates had not missed a game in 2018 after establishing himself in Murty's starting lineup.