Laidlaw was forced off in the 24th minute of Scotland's bruising 22-16 defeat to France in Paris on Sunday and left the stadium wearing a protective boot.
The Gloucester scrum-half, who is from Jedburgh in the Scottish Borders, was injured in their defeat to France. He was then released back to Gloucester for an assessment, and doctors have confirmed ligament damage and that he will play no further part in the tournament.
Scotland have been dealt a blow with captain Greig Laidlaw being ruled out of the rest of their Six Nations campaign.
While Finn Russell took over the kick duties, the loss of the 31-year-old is a significant blow to head coach Vern Cotter. "We have a group of leaders who can shoulder the burden".
"They have that experience and the more experienced members of the squad will also be able to take the pressure off here and there".
Glasgow Warriors scrum-half Ali Price is likely to take over when Scotland clash with Wales at BT Murrayfield.
As well as the dilemma over the captaincy, Cotter also faces a hard choice replacing his talismanic scrum-half.
Scotland, who beat Ireland in their Six Nations opener before defeat to France, are now fifth in the standings. "There are other things we can look at to improve on in the next game". "There's always someone else coming up, so it's about keeping an even keel".