"I've got a lot of rehabilitation and physiotherapy to go through but the good news is that there's no structural damage or need for an operation," said Warburton, whose injury has been diagnosed as nerve damage,.
"It is six weeks to the end of the season and eight weeks to the Wales tour so, if everything goes well, I should be OK for the trip to Australia - it could have been better news, but it also could have been worse.
"The same happened at the end of last year's Six Nations when I was out and couldn't play for the Blues for six weeks. I don't really know whether I will be able to play for the club again before the end of the season but we will be talking about that over the next few days."
With Martyn Williams also struggling with a rib cartilage injury, the Blues may have to give former Wales Under 20 cap Josh Navidi a first Heineken Cup start at No 7 against a Leinster back row trio of Shane Jennings, Jamie Heaslip and Sean O'Brien.
Better news for Blues coaches Justin Burnell and Gareth Baber is that second row Bradley Davies finishes his seven week suspension this week following his citing for a tip-tackle in Wales' win over Ireland at the Aviva Stadium last month.