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.
A pioneering strength and conditioning programme has been delivered to more than 8000 boys and girls at hub schools throughout Wales this season, helping to develop stronger, more flexible athletes for rugby and other sports.
The Singha Premiership Rugby 7s Series returns to the BT Sport Cardiff Arms Park on July 22nd when all four Welsh regions go head to head. Scarlets skills coach Dai Flanagan and Blues Elite Performance Pathway Manager Richard Hodges along with current Welsh squad members were at the launch of this season's event
GB7s women left their England base to train in Wales this week. Olympic Games hopeful Rachael Burford gives WRU TV's Graeme Gillespie her thoughts on Welsh teammate Jasmine Joyce - a 'one touch wonder'
The GB7s women's squad is currently training at Wales' Centre of Excellence where assistant coach Richie Pugh tells WRU TV's Graeme Gillespie some 'tough calls' will have to be made when it comes to finalising the 12 spots for Rio's Olympic Games.