Thomas, who won the most recent of his seven Wales caps in 2009, was treated by club medics before being transported by ambulance to Morriston Hospital in Swansea.
The 29-year-old has undergone "successful surgery" and is now in a "comfortable condition" but he will remain in hospital during his recovery.
Scarlets chief executive Mark Davies said: "All our thoughts and best wishes as Scarlets are with Rhys and his wife Paula and their family and the region will be keeping in close contact with medical teams at Morriston Hospital as to his progress but it is understood that he is comfortable and doing well.
"I am sure the whole rugby community in Wales would join with us in expressing to Rhys - all our very best wishes for a quick and comfortable recovery."
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