Thomas was substituted at half-time on Saturday at the Stade de France and had to watch from the sidelines as his team made a remarkable comeback which saw Wales clinch their third win on the trot in this year's tournament.
"It looks as if Gareth will be out for a number of weeks with the fractured thumb," said Wales Coach Mike Ruddock. "It means that he will almost certainly miss Scotland and Ireland and that will be a real blow. We will miss him, he has been an inspiration for us and all the boys will want to win for him.
"With Gareth missing I would think Michael Owen will be our Captain. He did a great job in the second half in France. He has been Vice-Captain all along throughout the championship."
Replacement hooker Robin McBryde, who played such a vital role in repelling France in the dying minutes in Paris, has also picked up a knee injury and it appears he will also miss the clash with Scotland at Murrayfield.