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 TV were on hand at the launch of a major new commercial deal with WRU and Mercedes-Benz South Wales (part of the Sinclair Group), which sees the family company become an official supplier to the Welsh Rugby Union
On the back of the recent Women's Rugby World Cup, the WRU has launched a revitalised Women's and Girls domestic seasonal structure, and the future is looking bright.
Go to www.wru.co.uk/tryourgame for more information
Roger Lewis talks to WRU TV at the announcement of a new £60 million Rugby Services Agreement (RSA) which provides a new and positive contractual relationship between the WRU and its four Regions for the next six years has been agreed.
The Welsh Rugby Union has announced a major new sponsorship deal with Gullivers Sports Travel which will make the UK's leading, and longest established, multi-sport tour operator, an Official Supplier for the rest of the decade.
Having taken part in seven World Cups as a player and coach, Liza Burgess hopes to go out in style this afternoon when Wales take on Australia in the Play-off for seventh and eighth place in the Women's Rugby World Cup in Paris.