Thomas, who had filled in during Nick Robinson's absence, will miss at least three weeks after damaging the AC-joint in his right shoulder during last weekend's defeat to Leinster.
It is yet another blow for the Blues who are already down to a skeleton team amid a catalogue of injuries and will leave coach Dai Young with third-choice fly-half Nick MacLeod for Monday's local derby against Newport Gwent Dragons at Rodney Parade.
Thomas said: "It couldn't have come a worst time, I'm gutted. I'd had a run of games in the starting team and there are some crucial fixtures coming up. This is going to be a very frustrating Christmas."
The Blues will also be without centre Jon Bryant, who made his debut for the club on Saturday, under the conditions of his move from the Dragons last week. However Tristan Davies made his return from a hand injury against Leinster and looks set to start.
The annual Women's club launch was held at the Wales Centre of Excellence where National Women's Head Coach and Programme Lead Rhys Edwards, Competition Secretary Adrian Howell and Cardiff Met player Ffion Jones express eagerness for the new campaign to get under way.
WRU TV follows Wales' RWC training squad on day one of their camp in North Wales. The squad were greeted to an official welcome in Colwyn Bay and then headed for an afternoon of team building at ZipWorld