The 31-year-old departed the Stade de France on crutches following his side's 22-16 defeat and it was initially claimed that he would not recover in time to play again in the current championship.
Those fears have come true for Scotland, as Gloucester Rugby scrum-half Laidlaw sustained ligament damage against Les Blues and will not feature in the remaining games with Wales, England and Scotland over the next month.
"A scan undertaken at his club, Gloucester, confirmed the clinical suspicion that the 58-times capped scrum-half sustained ligament damage midway through the first half of Sunday's test match against France," a Scotland statement read.
"The extent of the damage is such that he will take no further part in the current championship. 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 in their Six Nations opener before defeat to France, are currently fifth in the standings.