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.
WRU International Skills Coach Jason Strange is a busy man, combining the new role with that of Wales Under 20 attack coach, Ebbw Vale head coach and continuing to teach at Ebbw Fawr Learning Community.
Warren Gatland and Sam Warburton look ahead to this week's crunch RBS 6 Nations tie against France, where the Wales skipper in particular is keen to make his mark, as Paris has proved a bleak place for him in the past.
Following their historic win over England, Wales Under 20 suffered a narrow, 36-34 loss to their Scottish counterparts last weekend, despite outscoring them by five tries to three. Watch the match highlights and reaction.
WRU TV go behind the scenes with the Wales squad as they put the final touches in place ahead of the clash against Scotland at Murrayfield. Follow the squad on their captain's run, the kickers visit to Murrayfield and Neil Jenkins' press conference