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.
Whenever Bedlinog tackle Penallta a massive fixure is guaranteed but this Sunday there will be even more emphasis placed on the two rivals when they contest the SSE Swalec Plate final at Principality Stadium.
Ahead of their SSE SWALEC Bowl Final clash with Taffs Well at Principality Stadium on Sunday, Burry Port share their #FABXV nomination with WRUTV in the search for Welsh rugby's greatest volunteers. Everyone can get involved by sending nominations via twitter to @WRU_Community using the hashtag #FABXV
Cardiff Blues prop Gethin Jenkins and Ospreys centre Ben John look ahead to the first game at Principality Stadium in Saturday's double header which is promising to be a special occasion for all Welsh fans.
Carmarthen Quins Director of Rugby Ian Jones and committee member Jeff Thomas along with Llandovery chairman Handel Davies look ahead to Sunday's SSE SWALEC Cup showdown where both teams are out to prove 'West is best'
SWALEC ambassador Shane WIlliams is looking forward to Sunday's Finals Day where the Cup, Bowl and Plate offers a great opportunity for players and teams to experience the magic of playing at Principality Stadium
Carmarthen Quins coach Richard Kelly believes it is an exciting time to be part of the Scarlets region as his side take on local rivals Llandovery in the SSE Swalec Cup final on Sunday, as WRU TV's Graeme Gillespie discovers