The Wales captain has been suffering with a chest infection and will sit out the game on medical advice.
Josh Navidi will fill Warburton's number seven shirt, with Robin Copeland taking over the blindside role and Luke Hamilton on the bench.
Warburton's absence is the latest blow to hit the Blues who are also without Jamie Roberts, Leigh Halfpenny, Bradley Davies, Michael Paterson, Dan Fish, Andi Kyriacou and Tom James for the Pool Six clash.
A Cardiff Blues statement read: "Cardiff Blues have been dealt a blow with the news that Sam Warburton has pulled out of today's match due to a chest infection
"Warburton, who has just returned to the Blues from international duty with Wales, has been suffering with a chest infection at the latter part of the week and has been advised by medical staff to rest."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.