The right-winger has missed City's last two games with a calf injury and was set for a return to the team at Carlisle on Saturday, but an achilles problem will now rule him out.
Peter Taylor revealed: "Jason had trained well earlier this week and it looked like he would be okay for Saturday. But then he suffered an injury yesterday.
"At first, we thought the calf problem had flared up again but it looks to be a fresh injury to his achilles.
"If that's the case, he could be out for two weeks. It is a setback but we're fortunate that we have the strength-in-depth to cope."
Ryan France has been deputising in Price's absence, while Jon Walters, Danny Allsopp, Stuart Green and Lee Marshall are also options to fill the wide right positoin.