Patchell, 20, is now set for surgery on the injury, along with an operation on his shoulder, and is expected to miss several months of rugby as he commences his rehabilitation.
Phil Davies, Director of Rugby, said: "It is a disappointment to us to lose Patch for this period of time when he is playing so well, with many crucial games coming up in both Europe and the RaboDirect PRO12.
"However, it will give others within our squad the opportunity to step up as we look to enjoy a strong start to 2014.
"We wish Rhys all the best with his rehabilitation, will give him the very best support and I know he will be determined to get back fit as soon as possible. We all look forward to seeing him back in a Cardiff Blues jersey in the coming months."