The 83-times capped full-back will have an operation on Monday to insert a plate and screws to mend the break, meaning he will miss the remaining championship clashes against Scotland, on March 13, and Ireland six days later.
The injury forced Thomas off at half-time so he missed his side's remarkable second-half comeback which saw Wales win 24-18 - their third win on the trot.
"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."
Thomas is one of those tipped to skipper the Lions on the summer tour to New Zealand, seemingly vying with Ireland's Brian O'Driscoll and Paul O'Connell and England's Jonny Wilkinson for the honour.
It is unclear whether his absence from Wales' championship run-in will affect his captaincy chances.
Wales were also assessing a knee injury to replacement hooker Robin McBryde, who played such a vital role in repelling France in the dying minutes in Paris.
After initial medical reports it appears McBryde will miss the Scotland clash.