Warburton, who already has an Amlin Challenge Cup winners' medal in his collection, damaged his right shoulder in last weekend's home win over France and failed to appear for the second half - just as he did in the win over Ireland in Dublin.
"I'm still not sure in which incident the injury occurred, but there was no way I was going to be able to carry on in the second half. It was just too painful and I couldn't lift my arm above my head," said Warburton.
"The initial scans showed there was no structural damage, but I'm going back to see a specialist to try to get an idea on how long I might be out. It could be two weeks or two months, I just don't know.
"There are lots of big matches coming up with the Blues between now and the end of the season and I'd love to be fit to play in the Heineken Cup quarter-final in Dublin. I haven't played in the knock-out stages of the Heineken Cup before and it is going to be a huge game at the Aviva."
The Blues should have the rest of their Welsh contingent in tow, however, with triple Grand Slam prop Gethin Jenkins leading the way. The 2012 RBS 6 Nations leading points scorer, Leigh Halfpenny, new wing sensation Alex Cuthbert, centre Jamie Roberts, scrum half Lloyd Williams and lock Bradley Davies will also be hoping to make life difficult for the champions.
Leinster, who only have a handful of tickets left for the game at a stadium where they have yet to lose, have welcomed back their captain Leo Cullen and Ireland skipper Brian O'Driscoll into full training after operations and both players are likely to have at least one run out before head coach Joe Schmidt selects his team for the quarter-final.
Cullen and O'Driscoll are chasing their third Heineken Cup winners medals with Leinster - Cullen also picked up a runners-up medal with Leicester Tigers - and victory at the Aviva would earn the champions a trip to face either Saracens or ASM Clermont Auvergne.
Saracens will be without Namibian international Jacques Burger, who is sidelined for the rest of the season, but will have no fewer than seven players in their ranks who figured in the RBS 6 Nations as they prepare to meet Clermont at Vicarage Road on Sunday, 8 April (kick-off 4.30pm).
Four-time Heineken Cup winners Toulouse, who travel to Edinburgh for the biggest club game in Scottish history on Saturday, 7 April (kick-off 3.00pm), have lost French international full back Maxime Medard for the rest of the season with a knee injury and are sweating on the fitness of the tournament's top try scorer, Vincent Clerc. He damaged his shoulder in France's defeat to England and is struggling to recover in time for the trip to the Scottish capital.
Top seeds Munster, who went through their Pool campaign undefeated for the first time, have two-time winner David Wallace back in action after missing the first-half of the season, but have skipper Paul O'Connell and his Ireland team mate Conor Murray facing a race against time to recover from knee injuries picked up in the 6 Nations ahead of their sell-out Thomond Park quarter-final showdown with Irish rivals Ulster on Sunday, 8 April (kick-off 1.45pm).
Players likely to be involved in the high-profile Heineken Cup quarter-finals in less than three weeks time who featured in the 6 Nations are:
LEINSTER RUGBY (12) Rob Kearney, Gordon D'Arcy, Jonathan Sexton, Cian Healy, Mike Ross, Sean O'Brien, Jamie Heaslip, Sean Cronin, Eoin Reddan, Fergus McFadden, David Kearney, Shane Jennings
TOULOUSE (9) Thierry Dusautoir, Vincent Clerc, Florian Fritz, William Servat, Jean-Baptiste Poux, Louis Picamoles, Yoann Maestri, Lionel Beauxis, Clement Poitrenaud
ASM CLERMONT AUVERGNE (9) Aurelien Rougerie, Wesley Fofana, Julien Malzieu, Vincent Debaty, Julien Bonnaire, Julien Pierre, Morgan Parra, Jean-Marcellin Buttin, Gonzalo Canale
EDINBURGH RUGBY (9) Ross Ford, Lee Jones, Nick de Luca, Allan Jacobsen, Ross Rennie, David Denton, Geoff Cross, Mike Blair, Greig Laidlaw
CARDIFF BLUES (8) Sam Warburton, Leigh Halfpenny, Alex Cuthbert, Jamie Roberts, Gethin Jenkins, Bradley Davies, Lloyd Williams, Dan Parks
MUNSTER RUGBY (8) Paul O'Connell, Keith Earls, Conor Murray, Donncha O'Callaghan, Donnacha Ryan, Peter O'Mahony, Ronan O'Gara, Tomas O'Leary
SARACENS (7) Brad Barritt, Owen Farrell, David Strettle, Charlie Hodgson, Mouritz Botha, Matt Stevens, Rhys Gill
ULSTER RUGBY (4) Andrew Trimble, Rory Best, Stephen Ferris, Tom Co