The injurt was picked up in during Wales 42-0 thrashing of the Barbarians last month, but had hoped to join Wales for Saturday's second Test.
The newly signed Toulouse player still hopes to recover in time to join the squad in South Africa for the final Test of the tour on 26 June.
"I'm in contact with physio Mark Davies [in Wales] about Gareth Thomas' situation," said Wales coach Mike Ruddock
"It's still 50-50 whether he joins us in South Africa, but I have to say it's not looking too good at the moment."
There are no new injuries in the squad after last Saturday's 50-44 loss to the Pumas in Buenos Aires, but a stomach upset has laid low Williams, Mefin Davies, Dwayne Peel, Alix Popham and Peter Sidoli.