The centre suffered a knee injury in the Blues' PRO12 win over the Newport-Gwent Dragons in December.
"The knee injury has just plagued him a little bit longer than we thought," Cardiff boss Gareth Baber told BBC Sport.
"Unfortunately I don't think he's going to be able to win the race to get himself into a position to train this week and partake in the game on the weekend."
"There's a little break between our last European game and the Six Nations, but that will be up to the Union obviously when he joins up with them to see how he progresses," he said.
Cardiff are currently level on points with Edinburgh at the top of Heineken Cup Pool two.