Thomas suffered the injury during Wales' 32-20 defeat to Australia on Saturday - but he was still named in the side for this evening's Pool B game at the Millennium Stadium.
Head coach Gareth Jenkins had hoped Thomas would be make a suitable recovery.
Confirmation he had been withdrawn from the side came less than 24 hours before kick-off.
Jenkins said: "We have consulted specialist advice about Jon's injury and reached the conclusion that it would be wrong to risk him.
"We are blessed with a wealth of strength in our back row and are able to call on two former British Lions to come into the matchday squad in Martyn and Michael Owen.
"Michael comes onto the bench to cover both the back and second row and Colin Charvis switches flanks with Martyn coming into the team on the open side.
"The change of personnel should not affect the balance of our pack and we look forward to Jonathan returning to full training next week."
Thomas has not taken part in training all week and Wales team physio Mark Davies added: "Jonathan has been withdrawn as a precaution.
"The injury requires a period of rest without contact and has prevented him from taking a full involvement in training this week.
"It should, however, allow him to be fully involved next week."