The injury requires surgery, ruling him out of the remainder of the tournament.
Fellow centre Jonathan Davies faces a battle to regain his fitness for Wales' next match against France in Cardiff on February 21.
He is coming back from a pectoral injury suffered against South Africa in early November but coach Warren Gatland said he needed to show significant improvement to be considered for selection.
"He has been re-scanned. He is still a little bit sore at the moment," Gatland told the Six Nations website (www.rbs6nations.com).
"We are not too sure at the moment whether he will be available against France. He is still not 100 percent.
"He played that game for the Scarlets last week and felt a little bit sore, so we are trying to assess him to get up to speed in terms of lifting weights and contact. He is not there at the moment, so he is not available at the moment."
Wales are bidding to become the first team to win three consecutive Six Nations titles outright.
They beat Italy in their first match before being comprehensively beaten by the Irish.
(Reporting by Josh Reich)
