The Edinburgh Rugby player - who was injured during Friday's league victory over Llanelli Scarlets - will be out for six to eight weeks.
Such an absence will see him miss Scotland's first two games against England and Wales at least, and his participation in the remainder of the tournament is in doubt.
Scotland coach Frank Hadden now faces a major problem at scrum-half with Blair's rival for the position, Chris Cusiter, also on the injury list.
Cusiter has been out of action since dislocating his shoulder in the Scots' victory over Pacific Islanders in November.
He said yesterday it was "very unlikely" he would be back for the Calcutta Cup clash on February 3, with the earliest possible return being the Wales game at Murrayfield.
Gloucester scrum-half Rory Lawson and Glasgow counterpart Sam Pinder made their Test debuts from the bench last year and could be in contention for a start at Twickenham.
But Pinder is being kept out the Warriors team by veteran Craig Beveridge.
There was better news for Hadden as Blair's Edinburgh team-mate Rob Dewey was handed a boost in his recovery from the knee injury suffered during his try-scoring debut in the autumn Test win over Romania.
A check-up revealed the centre is ahead of schedule in his rehabilitation and should return to full training next week.