Thomas was taken to hospital on Sunday night suffering from a severe migraine and the full extent of his problem was revealed after he underwent an MRI scan.
Thomas will miss Wales' Six Nations clashes against Ireland, Italy and France, with number eight and fellow Lion Michael Owen now expected to lead his country for the remainder of this season's tournament.
Thomas had hoped to travel with the Wales team to Ireland later this week, but that will now not happen as the medical advice is that he continues to rest.
"Gareth Thomas has sustained damage to an artery in his neck," said Wales team doctor Professor John Williams.
"This caused the symptoms that he experienced on Sunday night and resulted in his admission to hospital.
"Those symptoms have since resolved. He has undergone detailed investigations and has been reviewed by a consultant neurologist at the University Hospital of Wales.
"The damaged blood vessel now needs to be given time to heal before Gareth can resume training and eventually playing. We are expecting him to make a full recovery and it is envisaged he will be able to resume training after 10 to 12 weeks."
Thomas complained of a severe migraine on Sunday night, not long after he had appeared on a BBC Wales television programme.
He attended the Princess of Wales Hospital in Bridgend but was then allowed home to rest.
Caretaker Wales coach Scott Johnson added: "We need to do what is in the best interests of Gareth Thomas in this situation, listen to the doctor's advice and leave him at home to rest.
"We will all be thinking of him but his personal health is of a much higher priority to us than anything that can happen on a rugby pitch.
"We wish him a speedy recovery and hope to have him back with us soon."