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The injury comes as a major blow to Wales as they prepare to travel to Italy in their first match of the tournament on Saturday 15 February, but Hansen will not be adding fly-half cover to the 31-man squad named earlier this week.
"It's not likely that we will call anyone in to replace Stephen," said Wales coach Steve Hansen. "It's obviously disappointing to lose a player of his calibre and it is a blow to our preparations."
"We hope Stephen a speedy recovery and hope he can be back with us as soon as possible."
Jones has scored 93 points in the Heineken Cup pool stages, just eight behind tournament top scorer Lodovic Mercier.
Jones is expected to be back in time for Llanelli's Heineken Cup quarter-final against Perpignan on April 11.
