Warburton, who led the British & Irish Lions to a drawn series with New Zealand in the summer, exacerbated the injury in training this week.
He’s undergone scans and has been reviewed by a consultant who confirmed the management plan that means he will likely miss four months.
“It’s a major blow for all concerned, it’s a blow for Cardiff Blues and Wales. We all hoped he would be back playing soon,” said Cardiff Blues boss Danny Wilson.
“It is a long-standing issue that he has had. He gets pain and discomfort on and off. The feeling was that two months off would help it settle completely and do him a world of good.
“He came back feeling confident about it. He went through the protocols when he came back to training and during the contact element, just on pads, it began to flare up again. We looked into it in more detail and it has led to where we are.
“He is obviously extremely frustrated. He thought that after two months he would come back really fresh and that is not the case but this is the right thing for him to do.
“He’s a very good professional and I’m sure he will apply himself to his usual standards.”