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 Hansen. 'It's obviously disappointing to lose a player of his calibre and it is a blow to our preparations, but we have enough cover within the squad in that position to make it unnecessary to call on anyone else at this late stage.'
Cardiff's Iestyn Harris and Pontypridd's uncapped Ceri Sweeney are the other two named fly half's in the Wales squad.
'It goes without saying that we hope Stephen a speedy recovery and hope he can be back with us as soon as possible, but this is now an opportunity for Ceri and Iestyn to step up,' added Hansen.