The 25-year-old was forced off during Saturday's 24-15 defeat to South Africa after suffering a pectoral injury in the 13th minute.
Wales coach Warren Gatland told reporters: "Jonathan Davies has done a pec which will probably keep him out for the rest of the campaign.
"He was a big loss to us in the first half as he had made a couple of breaks. He is a pretty important player to us at the moment and he is pretty disappointed.
"I have just spoken to the physio and they said it might settle and he could be back in December. If he needs an operation it could be five months and out of the Six Nations as well. We will wait and see what happens."
Davies has been capped 37 times by Wales, scoring 45 points in the process. He has also represented the British and Irish Lions on three occasions.