The scrumhalf was injured in the first half of Scotland’s 22-16 defeat by France at the Stade de France in Paris on Sunday and left the stadium on crutches.
“The extent of the damage is such that he will take no further part in the current championship,” the SRU said in a statement.
“Laidlaw will see a specialist later in the week to determine the best course of management and estimated time out of the sport.”
Scotland, who beat Ireland 27-22 in their first game, face Wales at Murrayfield in the third round on 25 February.
