Elias has missed the last three Scarlets' games and head coach Dwayne Peel says he will not play in the next two matches against Bayonne and Bulls.
When asked whether he will be fit for the Six Nations, Peel said: "Potentially, I am not sure where he is going to be for that."
Wales head coach Warren Gatland names his Six Nations squad on 17 January.
Elias, 27, misses the Challenge Cup trip to face Bayonne on 21 January and the United Rugby Championship (URC) home game against Bulls six days later.
The following weekend, Wales face Ireland in the Six Nations opener in Cardiff on 4 February.
"He's alright, I think it's going to be a medium-term (injury) for Ryan," added Peel.
"We need to get those Achilles right because he has been struggling for a while with them.
"It was a case of having to bite the bullet on this because to be fair to Ryan, he is a tough boy and wants to play through pain.
Elias, Ken Owens and Bradley Roberts were the three hookers in the autumn international squad selected by previous Wales head coach Wayne Pivac.
Ospreys hooker Dewi Lake was initially named by Pivac but was replaced by Roberts after suffering a shoulder injury which forced him to miss the November campaign.
Lake has returned to fitness but Sam Parry and Elliot Dee are currently injured.
Gatland has other injury concerns before the Six Nations starts. Dragons second row Will Rowlands and Ospreys fly-half Gareth Anscombe have been ruled out of the tournament with shoulder injuries, while Gloucester wing Louis Rees-Zammit is set to miss the first two matches because of an ankle problem.
Ospreys flanker Dan Lydiate is sidelined with a broken arm and will be out until February and Scarlets prop Samson Lee is a long-term casualty with an Achilles problem.
Cardiff centre Willis Halaholo is not expected to return until March because of a hamstring issue, while flanker Thomas Young is out for three months with a calf injury.
Dillon Lewis, Josh Navidi, Josh Macleod, Ben Carter, Owen Watkin and Johnny Williams are also battling to prove their fitness for the start of the tournament.
Ospreys centre George North has recovered from minor facial surgery and has been named as a replacement in the Heineken Champions Cup game against Montpellier.
Cardiff full-back Liam Williams went off in the defeat against Ospreys on 7 January and will miss the Challenge Cup match against Newcastle eight days later as he goes through head injury protocols.
One Wales player who has returned is British and Irish Lions prop Wyn Jones, impressing as a replacement in the Scarlets' 20-17 win over Cheetahs.
Jones, 30, has been absent for three months with a knee injury and missed the autumn internationals.
"It has been a frustrating three months," said Jones.
"It is always the same when you are on the sidelines, you want to be out on the field.
"It was nice to get some minutes under the belt. For myself, the most important thing is to get out on the field, enjoy my rugby and get back to full fitness."