The Wales Grand Slam captain injured his shoulder during the 16-9 victory over France that clinched the RBS 6 Nations title.
Warburton is likely to be out of action until May, but could make an appearance at the tail end of Cardiff Blues' season and hopes to tour Australia in June.
The Cardiff Blues flanker is also front-runner to lead Lions 'Down Under' in 2013.
"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."
The Blues face Leinster at the Aviva Stadium in the Heineken Cup quarter-finals on April 7, and with former Lion Martyn Williams struggling with a rib cartilage injury, the Blues may have to hand former Wales Under 20 cap Josh Navidi a first Heineken Cup start.
But 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.