The veteran prop will be out of action for another month after suffering achilles tendon damage during the autumn Test series.
Murray has not played for Worcester Warriors since the November internationals against Japan, South Africa and Australia and it looks very unlikely that the former British & Irish Lion will be fit to play before the latter stages of the tournament at best.
Dean Ryan, the Worcester's director of rugby, said: "I don't expect to have Euan back for at least four more weeks. He is still being troubled by his achilles, which had to be stripped out after his last stint with Scotland. Euan is still in pain and hasn't yet been able to run, so it is not a short-term problem."
Murray would not have been in the plans of Scott Johnson, the interim head coach, for the RBS 6 Nations opener against Ireland in Dublin on February 2 because he opts out of playing on Sundays because of his religious beliefs.
Even if his recovery is quicker than Ryan expects, Murray will have little opportunity to prove his match fitness before the game against England at Murrayfield the following weekend, or the fixture against Italy in Rome on February 22.
Scotland's other games are at home to France on March 8 and against Wales in Cardiff a week later.