"I haven't had an update on Sam but I'm led to believe it could be three or four months. The Blues medical staff haven't had a look at him, so they'll be working with the Lions medical staff to try to get him back into fitness as soon as possible," said Blues chief executive Richard Holland.
"We haven't got a timescale on it but given the message that was coming out of the Lions camp, he's got a period of rehabilitation. We've got an excellent medical team who will get him back ready as soon as we can.
"It's important that he rests up and takes a bit of time out and then we'll get him back into the Blues and see where we are."
Injuries have been a constant source of worry for Warburton during his four year international career, often marring the biggest occasions.
"I'm not sure what it is, but some of the biggest occasions in my career have been marred by injury or misfortune. I got sent-off early on in the World Cup semi-final, picked up a shoulder injury and had to go off in the 2012 Grand Slam game and was then in and out of the Welsh side in the 2013 championship season," explained Warburton.
"Then I get this injury ahead of the third Test. It always seems to happen to me around the big games."
The Blues are hoping that another of their Lions, Gethin Jenkins, will be fully fit for the start of the season. Jenkins was ruled out of his third tour with a calf injury before playing a game.