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."