Perry suffered the injury when he took a boot to the throat during Bristol's Heineken Cup victory over Harlequins at the Memorial Stadium on Sunday.
He was admitted to hospital last night for an operation to repair the damaged cartilage.
Bristol will not have a time-frame on Perry's likely return until a full assessment of the injury can be made but he is expected to be sidelined for weeks rather than months.
Perry must be considered doubtful for Bristol's vital Heineken Cup ties against Stade Francais and Cardiff in mid-January.
The injury will also hinder Perry's chances of winning a place in England's RBS 6 Nations squad.
Perry finished the game on Sunday but continued to feel discomfort in his throat and Bristol's medical chief Richard Mack was able to immediately diagnose the problem.
Remarkably, Perry's Bristol team-mate Nathan Budgett suffered the same freak injury against the Cardiff Blues in November.
Bristol head coach Richard Hill said: "When Budge suffered his injury, none of us had even seen an injury of this type before. For a second player to get injured in the same way barely a month later beggars belief.
"I feel for Shaun. He returned from the World Cup and got straight back to work with Bristol. He's been superb for us, has embraced his role as a senior player and I've had no hesitation naming him captain in Matt Salter's absence."
Bristol suffered a double blow in the Harlequins game, with England hopeful Dan Ward-Smith also forced to go under the knife this week after breaking a bone in his hand.
Ward-Smith was back in action after coming through an extensive rehabilitation programme after a major knee injury ruled him out of last season's 6 Nations and World Cup contention.
Hill added: "It's very unlucky for him. The last two seasons have been pretty wretched for him. It's tough for him."